
Given: ACB is the major arc of the circle. Angles AOB and ACB stand on the same arc. To prove: Angle AOB = 2 Angle ACB Proof: From triangle AOC, x = a+a (Exterior angle of a triangle) Hence x = 2a From triangle OBC, y = b+b Hence y = 2b Angle AOB = x + y Hence angAOB = 2(a+b) Hence Angle AOB = 2 Angle ACB
Example: Find angle a.
Directions: Solve the following 