Question

In the given figure, P is the centre of the circle.
Prove that : ∠XPZ = 2(∠XZY + ∠YXZ)

Answer 1

Arc XY subtends ∠XPY at the centre P and ∠XZY in the remaining part of the circle.
∠XPY = 2 (∠XZY)
Similarly,
Arc YZ subtends ∠YPZ at the centre P and ∠YXZ in the remaining part of the circle.
∠YPZ = 2 (∠YXZ)
Add both the results , we get
∠XPY + ∠YPZ = 2(∠XZY+∠YXZ)
∠XPZ = 2(∠XZY+∠YXZ)
Hence proved.