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Circle Theorems
20/09/2023
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vircbe theorenos •Angles at the CENTRE are twice the angle at the CIRCUMFERENCE EXAMPLES X 20 (168" Calculate the Missing angles x and y D y= 40(2) S 80° x=50 (2) =100° √5 x=168 = 84° Calculate the missing angles x and y y b 40° 100 2b x=100 = 50° angles in same segment The angles in the same segment are equal OR ↓ A EXAMPLES 52 40 B 0 54° Japo So S a P до Calculate the angles at p and q. p=52° q=40° The angles at the circumference subtended by the same are are equal find the size of angle C ACD = 54° 8 ACD Give a reason for your answer: • Angles in in the same segment are equal 0 CYCLIC Quadrilaterals a quadrilateral is drawn inside a circle every vertex (point) of the quadrilateral Must touch the circumference of the circle A EXAMPLES x ૧૫ 0 1990 Calculate the angles a and b. a 140 a = 60° .96° b = 140° ya c B Find the size of angles x and 84 +96 = 180° • opposite angles add up to 2180° 360-180 =180 6 60° 180 90° x and a 140 y = y. 90° angles in a serviciile •The angles at the circumference in a semicircle is a right angle. P EXAMPLES 4 N Angle APB =90 31° B diameter Calculate the angle z T = 90° 180 - Triangle ↓ 31 +90 = 180-121 = 59° z = 59° 121 مہ میں میں یہ مسمی۔ The augle (2.) Tangents which meet at the same point are equal in length EXAMPLES G 04 between a tangent and a radius is 90° perpendicular 45 06 A E C tangent Calculate the angles EFG and FOG FOG - 20+ FOG = 180 Ə FOG 160 E 6 = ∙B EFG atb = 180° 180-20-160° 160-80° 2 منهممسن • perpendicular from the centre of a circle to a chord bisects the chord. the chord EXAMPLES 5 см 4 A circle has a radius of 5CM. The chord Ef is 7CM. → How...
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Alternative transcript:
far is the midpoint of the chord from the centre of the circle?! fr M D 5cm 3.5cm Ass 5 3.S x M V a²=b²+c² 5²=3.5² + x² 25-12-25=x² 3.6=x ● alte Native segment the onem The angle between a tangent and a chord is equal to the Vangle in the alternative segment EXAMPLES Z 30, 9 y x C Calculate the Missing angles. ху z 30+x=90 x=60 Z=x 2=60 y: y=180-30-60 180-90 y = 90°