MathDB

Let

ABCD

be a cyclic quadrilateral with

AB<CD

. The diagonals intersect at the point

F

and lines

AD

and

BC

intersect at the point

E

. Let

K

and

L

be the orthogonal projections of

F

onto lines

AD

and

BC

respectively, and let

M

S

and

T

be the midpoints of

EF

CF

and

DF

respectively. Prove that the second intersection point of the circumcircles of triangles

MKT

and

MLS

lies on the segment

CD

.
(Greece - Silouanos Brazitikos)

Problem Statement