MathDB

A circle

\omega

with center

I

is inscribed into a segment of the disk, formed by an arc and a chord

AB

. Point

M

is the midpoint of this arc

AB

, and point

N

is the midpoint of the complementary arc. The tangents from

N

touch

\omega

in points

C

and

D

. The opposite sidelines

AC

and

BD

of quadrilateral

ABCD

meet in point

X

, and the diagonals of

ABCD

meet in point

Y

. Prove that points

X, Y, I

and

M

are collinear.

Problem Statement