MathDB

Nice geometry

Source: Bulgaria National Olympiad 2019

April 20, 2019

Circumcentergeometryorthocentercircumcircleperpendicular bisector

Problem Statement

Let

ABC

be an acute triangle with orthocenter

H

and circumcenter

O.

Let the intersection points of the perpendicular bisector of

CH

with

AC

and

BC

X

and

Y

respectively. Lines

XO

and

YO

cut

AB

P

and

Q

respectively. If

XP+YQ=AB+XY,

determine

\measuredangle OHC.