Let $M$ be a point inside square $ABCD$ and $A_1,B_1,C_1,D_1$ be the second intersection points of $AM$, $BM$, $CM$, $DM$ with the circumcircle of the square. Prove that $A_1B_1\cdot C_1D_1=A_1D_1\cdot B_1C_1$.
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Tags: geometry, circumcircle
Let $M$ be a point inside square $ABCD$ and $A_1,B_1,C_1,D_1$ be the second intersection points of $AM$, $BM$, $CM$, $DM$ with the circumcircle of the square. Prove that $A_1B_1\cdot C_1D_1=A_1D_1\cdot B_1C_1$.