CONO-SUR 2020 Problem 4

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 $DE$ .