In a ball with a radius of 10 cm, a section is drawn to find the radius of the section

In a ball with a radius of 10 cm, a section is drawn to find the radius of the section if the distance from the center of the ball to the section is 10 cm.

Let’s draw the diameter BC of the section and connect point O, the center of the ball, with points B and C.

Segments ОВ and ОC are the radii of the ball. ОВ = OC = R = 10 cm.

Then the triangle BOC is isosceles, and its height OH is also the median of the triangle BOC, therefore, BH = CH.

From a right-angled triangle BОH, according to the Pythagorean theorem, we determine the length of the leg BН.

BH ^ 2 = BO ^ 2 – HO ^ 2 = 10 ^ 2 = 8 ^ 2 = 100 – 64 = 36.

BH = 6 cm.

Answer: The section radius is 6 cm.