A ball with a radius of 5 cm is crossed by a plane 3 cm from the center of the ball.

A ball with a radius of 5 cm is crossed by a plane 3 cm from the center of the ball. Find the radius of the circle obtained in the section.

In order to find the unknown radius of the resulting figure, it is necessary to present a picture in a plane.
As a result of the section in the plane, a right-angled triangle will be obtained with the known:
1. Hypotenuse AC = 5 cm.
2. The leg, which will be equal to the distance from the center to the plane: AB = 3 cm.
Then the required radius will be equal to the unknown leg and will be found by the Pythagorean theorem:
BC = (AC * AC-AB * AB) ^ 0.5 = (5 * 5-3 * 3) ^ 0.5 = 4 cm.