In the figure, `P` is the centre of the circle. Prove that : `angle XPZ=2(angleXZY+angleYXZ)`.

Explanation

Since, arc `XY` subtends `angleXPY` at the centre and `angle XZY` at a point `Z` in the remaining part of the circle.
`therefore angle XPY =2angle XZY` ........(1)
Similarly, arc `YZ` subtends `angleYPZ` at the centre and `angleYXZ` at a point `X` in the remaining part of the circle.
`therefore angle YPZ=2angleYXZ`
Adding eqs. (1) and (2) , we have
`angle XPY+angle YPZ=2angle XZY+2angle YXZ`
`rArr angle XPZ=2(angle XZY+angle YXZ)`