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Square and equilateral triangles

Source: Romania JBMO TST 2024 Day 1 P2

July 31, 2024

geometrysquareEquilateral Triangle

Problem Statement

Let

M

be the midpoint of the side

AD

of the square

ABCD.

Consider the equilateral triangles

DFM{}

and

BFE{}

such that

F

lies in the interior of

ABCD

and the lines

EF

and

BC

are concurrent. Denote by

P{}

the midpoint of

ME.

Prove that"
[*]The point

P

lies on the line

AC.

[*]The halfline

PM

is the bisector of the angle

APF.

Adrian Bud

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