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: 3

1953 Moscow Mathematical Olympiad, 235
Tags: geometry , right isosceles , geometric construction , bisects segment
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.)

1974 All Soviet Union Mathematical Olympiad, 198
Tags: equal segments , right isosceles
Given points $D$ and $E$ on the legs $[CA]$ and $[CB]$, respectively, of the isosceles right triangle. $|CD| = |CE|$. The extensions of the perpendiculars from $D$ and $C$ to the line $AE$ cross the hypotenuse $AB$ in the points $K$ and $L$. Prove that $|KL| = |LB|$

1984 Tournament Of Towns, (059) A4
Tags: similar triangles , geometry , cut , right isosceles
Show how to cut an isosceles right triangle into a number of triangles similar to it in such a way that every two of these triangles is of different size. (AV Savkin)