3-6. Construct a right triangle given two medians drawn to the legs.

Construct a right triangle given two medians drawn to the legs.
Problem 6. Let $a$ and $b$ be the lengths of the medians, and $x$ and $y$ be the lengths of the legs. Then $\frac{x^{2}}{4}+y^{2}=a^{2}$ and $x^{2}+\frac{y^{2}}{4}=b^{2}$. Therefore, $x^{2}=\frac{16 b^{2}-4 a^{2}}{15}$ and $y^{2}=\frac{16 a^{2}-4 b^{2}}{15}$.

## VIII Olympiad (1945)

## First Round

## 7th - 8th Grades