Let
be a convex quadrilateral. A circle passing through the points
and
and a circle passing through the points
and
are externally tangent at a point
inside the quadrilateral. Suppose that
and
.
Prove that
.
%V0
Let $ABCD$ be a convex quadrilateral. A circle passing through the points $A$ and $D$ and a circle passing through the points $B$ and $C$ are externally tangent at a point $P$ inside the quadrilateral. Suppose that $\angle{PAB}+\angle{PDC}\leq 90^\circ$ and $\angle{PBA}+\angle{PCD}\leq 90^\circ$.
Prove that $AB+CD \geq BC+AD$.
Školjka