This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 2

1953 Moscow Mathematical Olympiad, 235
Tags: bisect segment , right isosceles , geometric construction , geometry
Divide a segment in halves using a right triangle. (With a right triangle one can draw straight lines and erect perpendiculars but cannot draw perpendiculars.)

1955 Moscow Mathematical Olympiad, 288
Tags: geometry , area , bisect segment , angles , right triangle
We are given a right triangle $ABC$ and the median $BD$ drawn from the vertex $B$ of the right angle. Let the circle inscribed in $\vartriangle ABD$ be tangent to side $AD$ at $K$. Find the angles of $\vartriangle ABC$ if $K$ divides $AD$ in halves.