In triangle ABC, it is known that AC = 40, BC = 30, angle C = 90. Find the radius of the circumscribed

In triangle ABC, it is known that AC = 40, BC = 30, angle C = 90. Find the radius of the circumscribed circle around this triangle.

The solution of the problem.

1. Angle c = 90 degrees, so the triangle abs is rectangular. The center of the circle circumscribed about a right-angled triangle is the midpoint of the hypotenuse. The hypotenuse is the diameter of the circle and half of the hypotenuse is the radius. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the legs.

2. Find the hypotenuse.

ab ^ 2 = bc ^ 2 + ac ^ 2;

ba ^ 2 = 40 ^ 2 + 30 ^ 2;

ba ^ 2 = 2500;

ba = 50;

3. Find the radius.

50: 2 = 25;

Answer: The radius of the hypotenuse is 25.