Question

in given figure p is the centre of circle. prove that angle xpz=2 (xyz+yxz)

Answer 1

We know that,angle subtended by an arc at the centre is double the angle subtended by the same arc at any point on the circle.Consider the minor arc XY, that subtends ∠XPY at the centre and ∠XZY at the circle.Now, ∠XPY = 2 ∠XZY .......(1)Consider the minor arc YZ, that subtends ∠YPZ at the centre and ∠YXZ at the circle.Now, ∠YPZ = 2 ∠YXZ .......(2)adding (1) and (2), wqe get ∠XPY + ∠YPZ = 2∠XZY + 2 ∠YXZ⇒∠XPZ = 2[∠XZY + ∠yxz )

Answer 2

Answer: Refer to attachment

Hope it helps