Netherland proposal for old IMO

[rsoldo]

A circle is inscribed in a rhombus. In each corner of the rhombus, a circle is inscribed such that it touches two sides of the rhombus and inscribed circle. These corner circles have radii $r_1$ and $r_2$ and the radius of the inscribed circle is $r$. If $r_1$ and $r_2$ are natural numbers and $r=r_1\cdot r_2$, find the value of $r_1,r_2$ and $r$.

[TOTAL]

$$\left( \frac{r_1-1}{r_1+1} \right)^2 + \left( \frac{r_2-1}{r_2+1} \right)^2=1$$

Можно перебором найти, всего $4$ варианта перебрать.

[wrest]

TOTAL в сообщении #1694318 писал(а):

Можно перебором найти,

4 и 9