MathDB

Consider a convex pentagon

ABCDE

and a variable point

X

on its side

CD

. Suppose that points

K, L

lie on the segment

AX

such that

AB = BK

and

AE = EL

and that the circumcircles of triangles

CXK

and

DXL

intersect for the second time at

Y

. As

X

varies, prove that all such lines

XY

pass through a fixed point, or they are all parallel. Proposed by Josef Tkadlec - Czech Republic

Problem Statement