Points M and N lie on the surface of a sphere with a radius of 50 cm. find the distance from the center

Points M and N lie on the surface of a sphere with a radius of 50 cm. find the distance from the center of the ball to the segment MN If the length of this segment is 80cm

Draw an axial section through the center of the ball, point O and point M and H. Then МН is a chord, the triangle ОМН is isosceles, since ОМ = ОН = R = 50 cm.

Let’s build the height OK, which will be the desired distance.

The height of the OC is also the tin of the median of the OMN triangle, then MK = NK = MN / 2 = 80/2 = 40 cm.

From a right-angled triangle OKM, according to the Pythagorean theorem, OK ^ 2 = OM ^ 2 – HK ^ 2 = 2500 – 1600 = 900.

OK = 30 cm.

Answer: From the center of the ball to a segment of 30 cm.