Question

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

Answer 1

Answer:

Step-by-step explanation:

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)

Answer 2

Answer:

Hey mate here is your answer.....

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 )

hope it's helpful for you...