MathDB

<AQT= 90^o wanted, altitudes, circumcircle (2021 Kyiv City MO Round2 9.2)

Source:

February 14, 2021

geometrycircumcircleright angle

Problem Statement

In an acute triangle

AB

the heights

BE

and

CF

intersect at the orthocenter

H

, and

M

is the midpoint of

BC

. The line

EF

intersects the lines

MH

and

BC

at the points

P

and

T

, respectively.

AP

intersects the cirumcscribed circle of

\vartriangle ABC

for second time at the point

Q

. Prove that

\angle AQT= 90^o

.
(Fedir Yudin)