18.In the ngure. Pisthe centre ofthe circle, prove that APZ-2(A ZP +LY

1.	18.In the ngure. Pisthe centre ofthe circle, prove that APZ-2(A ZP +LYNZ).
Answer» 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 XZYangle XPZ = 2 ( angleYZX+angleXZY)( taking 2 as common)

18.In the ngure. Pisthe centre ofthe circle, prove that APZ-2(A ZP +LYNZ).

Answer»

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 XZYangle XPZ = 2 ( angleYZX+angleXZY)( taking 2 as common)