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Two circles C1a n dC2 intersect at two d...

Two circles `C_1a n dC_2` intersect at two distinct points `Pa n dQ` in a line passing through `P` meets circles `C_1a n dC_2` at `Aa n dB` , respectively. Let `Y` be the midpoint of `A B ,a n dQ Y` meets circles `C_1a n dC_2` at `Xa n dZ` , respectively. Then prove that `Y` is the midpoint of `X Zdot`

Text Solution

Verified by Experts

From the figure, `YP.YB=YZ.YQ`
and `YA.YP=YX.YQ`
But `YA=YB`
Hence, `XY=YZ`
So, Y is midpoint of XZ.
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