Question 7
Given a right-angled triangle $ABC$ with $AC = BC$, and $\angle C = 90^\circ$. Let points $M$ and $N$ belong to the sides $AC$ and $BC$ respectively; $MN = BC$. For each pair of such points $M$ and $N$ a circle passing through $M$, $N$ and touching the hypotenuse $AB$ is constructed.
Find the locus of the centers of these circles.
Find the locus of the centers of these circles.