Question

a 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 angle prq is equal to L and angle o p q is equal to M then find l + m

Answer 1

O is the centre of the circle PQ is a chord of the circle and R is any point on the circle if angle prq is equal to L and angle o p q is equal to M

∠POQ = 2∠PRQ  

⇒ ∠POQ = 2l    

In △PQO, OP = OQ = r  

⇒ ∠OQP = ∠OPQ = m  

Also, ∠OPQ + ∠OQP + ∠POQ  = 180°  

⇒ m + m = 2l = 180°  

⇒ 2(l + m) = 180°

⇒ l + m = 90°