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Reflections of A lie on BC

Source: Cono Sur Math Olympiad 2020 #4

December 4, 2020

geometrygeometric transformationreflectioncono sur

Problem Statement

Let

ABC

be an acute scalene triangle.

D

and

E

are variable points in the half-lines

AB

and

AC

(with origin at

A

) such that the symmetric of

A

over

DE

lies on

BC

. Let

P

be the intersection of the circles with diameter

AD

and

AE

. Find the locus of

P

when varying the line segment

DE

.

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