A right-angled triangle with a leg of 6 cm is inscribed surrounded by a radius of 5 cm. Find the rest of the sides of the triangle.

Let us determine what the length of the hypotenuse of this triangle should be equal to, when from the condition of the task we know that the radius of the circle described around it corresponds to 5 centimeters:
5 * 2 = 10.
Let us determine how long the unknown leg will be in this triangle, when from the condition of the problem we know that the length of the known leg corresponds to 6 centimeters:
√ (10 ^ 2 – 6 ^ 2) = √ (100 – 36) = √64 = 8.
Answer: Under such initial conditions, the length of the hypotenuse will be 10 centimeters, and the leg – 8.