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Isosceles triangle geo

Source: IMAR Test 2023 P1

December 16, 2023

geometry

Problem Statement

Let

ABC

be an acute triangle, and let

D,E,F

be the feet of its altitudes from

A,B,C

respectively. The lines

AB{}

and

DE

cross at

K{}

and the lines

AC

and

DF

cross at

M{}

Let

M

be the midpoint of the side

BC

and let the line

P{}.

cross the circle

(ABC)

again at

N{}.

The parallel through

M{}

to

EF

crosses the line

KL

at

P{}.

Prove that the triangle

MNP

is isosceles.

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