Question

Given: Circle k (O), OA and OC -radii, AP and CP - tangents, m∠AOC=150° Find: m∠APC

Answer 1

m∠APC = 30°

Explanation:

To solve for the above question, we would be making use of circle theorems

Looking at the circle, we can see that

m∠APC is an Angle outside the circle

m∠AOC is a smaller arc in the circle.

Therefore, Circle Theorem states that for a circle with two tangents,

The Angle outside the circle + The smaller arc = 180°

Hence,

m∠AOC + m∠APC = 180°

m∠APC = 180° - m∠AOC

m∠APC = 180° - 150°

m∠APC = 30°