MathDB

In the acute triangle

ABC

the orthocenter

H

and the center of the circumscribed circle

O

were noted. The line

AO

intersects the side

BC

at the point

D

. A perpendicular drawn to the side

BC

at the point

D

intersects the heights from the vertices

B

and

C

of the triangle

ABC

at the points

X

and

Y

respectively. Prove that the center of the circumscribed circle

\Delta HXY

is equidistant from the points

B

and

C

.
(Danilo Hilko)

Problem Statement