A convex quadrilateral
has perpendicular diagonals. The perpendicular bisectors of the sides
and
meet at a unique point
inside
. Prove that the quadrilateral
is cyclic if and only if triangles
and
have equal areas.
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A convex quadrilateral $ABCD$ has perpendicular diagonals. The perpendicular bisectors of the sides $AB$ and $CD$ meet at a unique point $P$ inside $ABCD$. Prove that the quadrilateral $ABCD$ is cyclic if and only if triangles $ABP$ and $CDP$ have equal areas.
Školjka