MathDB

The median

AM

is drawn in the acute-angled triangle

ABC

with different sides. Its extension intersects the circumscribed circle

w

of this triangle at the point

P

. Let

A {{H} _ {1}}

be the altitude

\Delta ABC

H

be the point of intersection of its altitudes. The rays

MH

and

P {{H} _ {1}}

intersect the circle

w

at the points

K

and

T

, respectively. Prove that the circumscribed circle of

\Delta KT {{H} _ {1}}

touches the segment

BC

.
(Hilko Danilo)

Problem Statement