A plane intersects a sphere that has a radius of 13 cm. The distance from the center of the sphere to the closest point on the plane is 5 cm. What is the radius of the circle that is the intersection of the sphere and the plane?

Question

A plane intersects a sphere that has a radius of 13 cm. The distance from the center of the sphere to the closest point on the plane is 5 cm. What is the radius of the circle that is the intersection of the sphere and the plane?
A. 8 cm
B. 10 cm
C. 12 cm
D. 13 cm

MathMate · Answer

Draw the figure and convince yourself that the radius of the circle is given by Pythagoras theorem r^2=sqrt(13^2-5^2)