Question

In the given figure, P is the centre of the circle. Prove that :

∠XPZ = 2 (∠XZY + ∠YXZ)

Explain with complete calculations & justifications.

Points : 20 ☺

Answer 1

see attachment...hope it helps......

Answer 2

In the figure,
angle XPY = 2 angle YZX _____(1)
since angle subtended by an arc at the centre is double the angle subtended by it on any other part of the circle.

angle YPZ = 2 angle XZY_______(2)
since angle subtended by an arc at the centre is double the angle subtended by it on any other part of the circle.

eq(1)+(2)
angleXPY+angle YPZ = 2angle YZX+ 2 angle XZY
angle XPZ = 2 ( angleYZX+angleXZY)
( taking 2 as common)


hope it helps...