In triangle ABC AC = 5, BC = 2√5, ∠C = 90 °. Find the radius of the circle around this triangle.

First, let’s find the length of the hypotenuse of a given right-angled triangle.

In the formulation of the condition for this task, it is reported that the lengths of the legs AC and BC of this right-angled triangle are 5 and 2√5, respectively, therefore, using the Pythagorean theorem, we can find the length of the hypotenuse AB of this right-angled triangle:

| AB | = √ (| AC | ^ 2 + | BC | ^ 2) = √ (5 ^ 2 + (2√5) ^ 2) = √ (25 + 4 * 5) = √ (25 + 20) = √45 = 3√5.

Since in any right-angled triangle the center of the circumscribed circle lies on the hypotenuse of this triangle and divides it in half, the radius of the circle circumscribed about this triangle is 3√5 / 2.

Answer: 3√5 / 2.