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Isogonality of P&reflection

Source: Baltic Way 2021, Problem 11

November 15, 2021

geometrygeometry proposed

Problem Statement

A point

M

lies inside a triangle

BC

. The points

K

and

L

are the projections of

P

onto

AB

and

AC

, respectively. The point

M

lies on the line

BC

so that

KM = LM

, and the point

P'

is symmetric to

P

with respect to

M

. Prove that

\angle BAP = \angle P'AC

.

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