## Task B-1.4.

The orthocenter of an isosceles triangle is located at one of the triangle's vertices. If the lengths of the legs are $3 \sqrt{2} \mathrm{~cm}$, what is the length of the radius of the circumscribed circle around this triangle?
## Solution.

The orthocenter is the vertex of the triangle if and only if the triangle is a right triangle. We conclude that the given triangle is a right triangle.

The radius of the circumscribed circle of a right triangle is half the hypotenuse.

$$
r=\frac{c}{2}=\frac{1}{2} \sqrt{2 \cdot(3 \sqrt{2})^{2}}=3
$$