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Midpoints and foot of altitude are collinear

Source: Centroamerican Olympiad 2016, problem 2

June 19, 2016

geometrycircumcirclehardCyclicconcurrency

Problem Statement

Let

ABC

be an acute-angled triangle,

\Gamma

its circumcircle and

M

the midpoint of

BC

. Let

N

be a point in the arc

BC

of

\Gamma

not containing

A

such that

\angle NAC= \angle BAM

. Let

R

be the midpoint of

AM

,

S

the midpoint of

AN

and

T

the foot of the altitude through

A

. Prove that

R

,

S

and

T

are collinear.

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