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:

(i) ∠ABC = 2∠APQ,

(ii) ∠ACB = 2∠APR,

(iii) ∠QPR = 90° - (1/2)∠BAC

Answer 1

Join PQ and PR