Given a right triangle $ABC$, where $\alpha=\frac{\pi}{2}$. Find a point $P$ on the hypotenuse such that the sum of the squares of the perpendiculars dropped from $P$ to the legs is equal to $m^2$.
The given distance $m$ is taken as the radius, and a circle with radius $m$ is drawn from point $A$ as the center. The intersection points of this circle with the line $BC$ are the sought $P$ points.

If the line $h=AD \perp BC$ is greater than, equal to, or less than $m$, the problem has no, one, or two solutions, respectively.

(Visnya Aladár, fóreálisk. VII. o. t. Pécs.)

The problem was also solved by: Engel Richárd, föreálisk. VII.o. t. Györ; Weisz Lipót föreáliskolai VI.ot.t.Pécs. Heymann Tivadar and Rosenberg József, fóreáliskola VIII. o. t. Györ.