Angles in a Semicircle

This section focuses on a specific case of angles in a circle: the angle in a semicircle. It introduces the important theorem that an angle inscribed in a semicircle is always a right angle (90°).

Definition: A semicircle is half of a circle, formed by a diameter and the arc it subtends.

The page provides a clear example demonstrating how to use this theorem in conjunction with other angle properties to solve more complex problems. This example involves calculating an unknown angle using the semicircle theorem and properties of triangles.

Highlight: The angle inscribed in a semicircle is always 90° (a right angle).

This theorem is particularly useful in identifying right angles in geometric figures and is often featured in circle theorems questions and answers.

Tangents to Circles

This page introduces two important properties of tangents to circles:

1. The angle between a tangent and a radius drawn to the point of contact is 90° (perpendicular).
2. Tangents drawn from an external point to a circle are equal in length.

Vocabulary: Tangent - A line that touches a circle at exactly one point.

The page provides an example problem that combines both of these properties, requiring students to calculate angles involving tangents and radii. This type of question is common in circle theorems and angles calculations GCSE exams.

Example: In a problem where two tangents are drawn from an external point, the angles between the tangents and the line joining the center to the external point are equal.

Understanding these tangent properties is crucial for solving more advanced circle theorem questions and problems involving complex geometric constructions.