Question

A triangle ABC is inscribed in a circle. The bisectors of angles BAC, ABC and ACB meet the circumcircle of the triangle at points P, Q and R respectively. Prove that : 

∠ACB = 2∠APR,

Answer 1

Join PQ and PR

CR is the bisector of ∠ACB

`=> ∠ACR = 1/2 ∠ACB`

Also, ∠ACR = ∠APR

(Angle in the same segment)

∴ ∠ACB = 2∠APR