The two most important circle theory we need to know when solving problems are:

CT1. The angle in a semicircle is a right angle (or, more formally, the angle subtended by the diameter of a circle equals 90 degrees)

CT2. The angle between any tangent of a circle and the radius of a circle that meets it is 90 degrees

Worked Example

AB is the diameter of a circle with C as its centre. D is any point on the circumference. Find out the size of angle ADB.

Exercise

Answers

1.) (a) x= 43, y = 43, z=94 (b) x=124, y = 34 (c) x=35 (d) x=48

2.) (a) x=41.5 (b) x=38

3.) (a) Tangents subtended from the same point are equal in length (b) (i) CAB=70 (ii) DAC=20 (iii)) ADC =70