MathDB

HX bisects AC, circumcircles, altitude (2020 Kyiv City MO Round2 9.2)

Source:

September 21, 2020

geometrycircumcirclebisects segmentaltitude

Problem Statement

In the acute-angled triangle

ABC

is drawn the altitude

CH

. A ray beginning at point

C

that lies inside the

\angle BCA

and intersects for second time the circles circumscribed circles of

\vartriangle BCH

and

\vartriangle ABC

at points

X

and

Y

respectively. It turned out that

2CX = CY

. Prove that the line

HX

bisects the segment

AC

.
(Hilko Danilo)