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Configuration with median and right angles

Source: EMC 2023 Junior P3

December 18, 2023

geometry

Problem Statement

Consider an acute-angled triangle

ABC

with

AB < AC

. Let

M

and

N

be the midpoints of segments

BC

and

AB

, respectively. The circle with diameter

AB

intersects the lines

BC, AM

and

AC

at

D, E

, and

F

, respectively. Let

G

be the midpoint of

FC

. Prove that the lines

NF, DE

and

GM

are concurrent.
Michal Pecho

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