The radius of a circle circumscribed about a rectangle of a triangle is 14.5 AB is equal to 21. Find another leg.

If a circle is described around a right-angled triangle, then its center lies on the hypotenuse and divides it in half.

From here we find the length of the hypotenuse of the triangle, which is equal to 2R. The length of the hypotenuse is 14.5 * 2 = 29.

Knowing the length of the hypotenuse and one leg, we find the length of the second leg.

c ^ 2 = a ^ 2 + b ^ 2,

b ^ 2 = c ^ 2 – a ^ 2;

b = √ (c ^ 2 – a ^ 2);

b = √ (29 ^ 2 – 21 ^ 2) = √ ((29 – 21) * (29 + 21)) = √ (8 * 50) = √400 = 20.

Answer: the length of the second leg is 20.