MathDB

Obtuse triangle with symmetric points

Source: 2018 Latvia BW TST P10

March 26, 2022

geometrycircumcircle

Problem Statement

Let

ABC

be an obtuse triangle with obtuse angle

\angle B

and altitudes

AD, BE, CF

. Let

T

and

S

be the midpoints of

AD

and

CF

, respectively. Let

M

and

N

and be the symmetric images of

T

with respect to lines

BE

and

BD

, respectively. Prove that

S

lies on the circumcircle of triangle

BMN

.

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