Two circles `C_1` and `C_2`
intersect at two distinct points `P`and`Q`
in a line passing through `P`
meets circles `C_1`and`C_2`
at `A`and`B`
, respectively. Let `Y`
be the midpoint of `A B` and `Q Y`
meets circles `C_1` and`C_2`
at `X`a n d`Z`
respectively. Then prove that `Y`
is the midpoint of `X Z`
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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