Question

Two circles C₁ and C₂ intersect at two distinct points P and Q in a plane. Let a line passing through P meet the circles C₁ and C₂ in A and B, respectively. Let Y be the mid-point of AB and QY meet the circles C₁ and C₂ in X and Z, respectively. Then

(A)  Y is the mid-point of XZ

(B)  XY/XZ = 2/1

(C)  YX = YZ

(D)  XY + YZ = 3Y

Answer 1

Correct option  (A), (C)

YP . YB = YZ . YQ and YA . YP = YX . YQ

But YA = YB. Hence, YX = YZ