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Jess Doyle
08/09/2025
Maths
Circle Theorems
796
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8 Sept 2025
•
Fun with Circle Angles: Easy Exercises and Cool Formulas
Jess Doyle
@elyodxj
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Teoremas de Ángulos en la Circunferencia
Esta página presenta varios teoremas cruciales relacionados con los ángulos en la circunferencia, proporcionando una base sólida para el análisis geométrico avanzado.
El primer teorema establece que el ángulo en el centro de un círculo es el doble del ángulo en la circunferencia cuando ambos subtienden el mismo arco. Este teorema es fundamental para relacionar ángulos centrales e inscritos.
Example: Si un ángulo inscrito mide 30°, el ángulo central correspondiente medirá 60°.
Otro teorema importante afirma que los ángulos inscritos en el mismo segmento de un círculo son iguales. Esto es crucial para entender la relación entre diferentes ángulos inscritos.
Highlight: Los ángulos opuestos en un cuadrilátero cíclico suman 180°. Esta propiedad es esencial para resolver problemas que involucran cuadriláteros inscritos en círculos.
La página también menciona que los ángulos en el mismo segmento de un círculo son iguales, lo que refuerza la importancia de los segmentos circulares en el estudio de los ángulos en la circunferencia.
Vocabulary: Un cuadrilátero cíclico es un cuadrilátero cuyos cuatro vértices se encuentran en la circunferencia de un círculo.
Estos teoremas son fundamentales para resolver ejercicios de ángulos en la circunferencia y son ampliamente utilizados en problemas geométricos más avanzados. Comprender estas relaciones es crucial para dominar los conceptos de geometría circular.
Propiedades Fundamentales de los Ángulos en la Circunferencia
Esta página introduce varias propiedades de ángulos en la circunferencia fundamentales, esenciales para comprender la geometría circular.
La primera propiedad establece que la línea perpendicular desde el centro de un círculo hasta una cuerda biseca dicha cuerda. Esto es crucial para entender la relación entre el centro del círculo y las cuerdas.
Definition: Una cuerda es un segmento de línea que conecta dos puntos en la circunferencia de un círculo.
Otra propiedad importante afirma que el ángulo entre una tangente y un radio en el punto donde la tangente toca el círculo es siempre un ángulo recto (90 grados).
Vocabulary: Una tangente es una línea que toca el círculo en exactamente un punto.
La página también menciona que los ángulos entre dos tangentes dibujadas desde un punto exterior al círculo son iguales. Esta propiedad es útil en problemas que involucran tangentes externas.
Highlight: El ángulo entre una tangente y una cuerda es igual al ángulo en el segmento alterno. Esta propiedad es fundamental para resolver muchos problemas de ángulos en la circunferencia.
Estas propiedades forman la base para comprender relaciones más complejas en la geometría circular y son esenciales para resolver ejercicios de ángulos en la circunferencia.
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Stefan S
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Samantha Klich
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Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
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Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Fun with Circle Angles: Easy Exercises and Cool Formulas
Jess Doyle
@elyodxj
Los ángulos en la circunferencia son un concepto fundamental en geometría que explora las relaciones entre ángulos formados por líneas y puntos en un círculo. Este resumen aborda las propiedades clave y teoremas relacionados con estos ángulos.
- Los ángulos en... Show more
Teoremas de Ángulos en la Circunferencia
Esta página presenta varios teoremas cruciales relacionados con los ángulos en la circunferencia, proporcionando una base sólida para el análisis geométrico avanzado.
El primer teorema establece que el ángulo en el centro de un círculo es el doble del ángulo en la circunferencia cuando ambos subtienden el mismo arco. Este teorema es fundamental para relacionar ángulos centrales e inscritos.
Example: Si un ángulo inscrito mide 30°, el ángulo central correspondiente medirá 60°.
Otro teorema importante afirma que los ángulos inscritos en el mismo segmento de un círculo son iguales. Esto es crucial para entender la relación entre diferentes ángulos inscritos.
Highlight: Los ángulos opuestos en un cuadrilátero cíclico suman 180°. Esta propiedad es esencial para resolver problemas que involucran cuadriláteros inscritos en círculos.
La página también menciona que los ángulos en el mismo segmento de un círculo son iguales, lo que refuerza la importancia de los segmentos circulares en el estudio de los ángulos en la circunferencia.
Vocabulary: Un cuadrilátero cíclico es un cuadrilátero cuyos cuatro vértices se encuentran en la circunferencia de un círculo.
Estos teoremas son fundamentales para resolver ejercicios de ángulos en la circunferencia y son ampliamente utilizados en problemas geométricos más avanzados. Comprender estas relaciones es crucial para dominar los conceptos de geometría circular.
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Propiedades Fundamentales de los Ángulos en la Circunferencia
Esta página introduce varias propiedades de ángulos en la circunferencia fundamentales, esenciales para comprender la geometría circular.
La primera propiedad establece que la línea perpendicular desde el centro de un círculo hasta una cuerda biseca dicha cuerda. Esto es crucial para entender la relación entre el centro del círculo y las cuerdas.
Definition: Una cuerda es un segmento de línea que conecta dos puntos en la circunferencia de un círculo.
Otra propiedad importante afirma que el ángulo entre una tangente y un radio en el punto donde la tangente toca el círculo es siempre un ángulo recto (90 grados).
Vocabulary: Una tangente es una línea que toca el círculo en exactamente un punto.
La página también menciona que los ángulos entre dos tangentes dibujadas desde un punto exterior al círculo son iguales. Esta propiedad es útil en problemas que involucran tangentes externas.
Highlight: El ángulo entre una tangente y una cuerda es igual al ángulo en el segmento alterno. Esta propiedad es fundamental para resolver muchos problemas de ángulos en la circunferencia.
Estas propiedades forman la base para comprender relaciones más complejas en la geometría circular y son esenciales para resolver ejercicios de ángulos en la circunferencia.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Mock Exam
Quiz
Flashcards
Essay
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user