MathDB

JBMO TST Bosnia and Herzegovina 2022 P3

Source: JBMO TST Bosnia and Herzegovina 2022

May 21, 2022

JBMO TSTgeometrycircumcirclenational olympiad

Problem Statement

Let

ABC

be an acute triangle. Tangents on the circumscribed circle of triangle

ABC

at points

B

and

C

intersect at point

T

. Let

D

and

E

be a foot of the altitudes from

T

onto

AB

and

AC

and let

M

be the midpoint of

BC

. Prove: A) Prove that

M

is the orthocenter of the triangle

ADE

. B) Prove that

TM

cuts

DE

in half.