The diameter of the circle circumscribed about a right-angled triangle is 10, and one of the legs is 6. Find the other leg.

Let us take advantage of the fact that the center of a circle circumscribed around any right-angled triangle lies on the hypotenuse of this triangle and divides it in half.

Consequently, the radius of a circle circumscribed around any right-angled triangle is half the hypotenuse of this triangle, and the diameter of this circle is equal to the hypotenuse.

In the initial data for this task, it is reported that the diameter of the circle circumscribed about this right-angled triangle is 10, therefore, the hypotenuse of this triangle is also 10.

Knowing the lengths of the hypotenuse and one of the legs, we find the second leg:

√ (10 ^ 2 – 6 ^ 2) = √ (100 – 36) = √64 = 8.

Answer: 8.