Question

In the given figure, O is the centre of the circle. PQ is a chord of the circle and R is
any point on the circle. If ∠PRQ = l and ∠OPQ = m, then find l + m.

Answer 1

∠POQ = 2∠PRQ  

⇒ ∠POQ = 2l    

In △PQO, OP = OQ = r  

⇒ ∠OQP = ∠OPQ = m  

Also, ∠OPQ + ∠OQP + ∠POQ  = 180°  

⇒ m + m + 2l = 180°  

⇒ 2m + 2l = 180°

⇒ 2(l + m) = 180°

⇒ l + m = 90°