Question

P is the centre of the circle. Prove that ang.XPZ=2 (ang. XYZ +ang. YXZ)

Answer 1

We know that angle subtended by the arc at the centre is double the angle subtended by it at any other point on the remaining part of circle.

⇒ ∠XOY = 2∠XZY ...(1)

and ∠ZOY = 2∠YXZ ...(2)



Adding (1) and (2) we get

∠XOY + ∠ZOY = 2∠XZY + 2∠YXZ

⇒∠XOZ = 2(∠XZY + ∠YXZ)