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Q.

Two circles C1 and C2 intersect at two distinct points P and Q in a plane. Let a line passing through P meets circle C1 and C2 in A and B respectively. Let Y is midpoint of AB and QY meets circle C1 and C2 in X and Z respectively then

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a

XYYZ=31

b

Y is the mid point of XZ

c

XY + YZ = 2YZ

d

XY = YZ

answer is A, C, D.

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Detailed Solution

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

But,it is given that

Y is the mid-point of AB
But YA = YB    ...(iii)

From (i) and (ii) we get,

yP⋅y0yA⋅yP=yz⋅yQyx⋅yQ iii
Hence XY = YZ

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Two circles C1 and C2 intersect at two distinct points P and Q in a plane. Let a line passing through P meets circle C1 and C2 in A and B respectively. Let Y is midpoint of AB and QY meets circle C1 and C2 in X and Z respectively then