MathDB

Let

ABCD

be a cyclic quadrilateral (a quadrilateral which can be inscribed in a circle). Let

E

and

F

be variable points on the sides

AB

and

CD

, respectively, such that

\frac{AE}{EB} = \frac{C}{FD}

. Let

P

be the point on the segment

EF

such that

\frac{PE}{PF} = \frac{AB}{CD}

. Prove that the ratio between the areas of triangle

APD

and

BPC

does not depend on the choice of

E

and

F

Problem Statement