MathDB

In a trapezoid

ABCD

such that the internal angles are not equal to

90^{\circ}

, the diagonals

AC

and

BD

intersect at the point

E

. Let

P

and

Q

be the feet of the altitudes from

A

and

B

to the sides

BC

and

AD

respectively. Circumscribed circles of the triangles

CEQ

and

DEP

intersect at the point

F\neq E

. Prove that the lines

AP

BQ

and

EF

are either parallel to each other, or they meet at exactly one point.

Problem Statement