MathDB

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.

Problem Statement