MathDB

Let

M

be a point on the arc

AB

of the circumcircle of the triangle

ABC

which does not contain

C

. Suppose that the projections of

M

onto the lines

AB

and

BC

lie on the sides themselves, not on their extensions. Denote these projections by

X

and

Y

, respectively. Let

K

and

N

be the midpoints of

AC

and

XY

, respectively. Prove that

\angle MNK=90^{\circ}

Problem Statement