MathDB

Let

ABCD

be a cyclic quadrilateral which is not a trapezoid and whose diagonals meet at

E

. The midpoints of

AB

and

CD

are

F

and

G

respectively, and

\ell

is the line through

G

parallel to

AB

. The feet of the perpendiculars from E onto the lines

\ell

and

CD

are

H

and

K

, respectively. Prove that the lines

EF

and

HK

are perpendicular.

Problem Statement