posted by Chica on .
A plane intersects a sphere that has a radius of 13cm. 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?
Could please shed some light on how this problem is worked out.
draw a cross-section diagram, that is,
draw a circle with radius 13
draw a chord which is 5 cm from the centre.
Draw a perpendicular from the circle to the plane.
You have 2 congruent right-angled triangles with hypotenuse 13 and side 5,
let the other side be x
x^2 + 5^2 = 13^2
x = 12
Since the chord is diameter of the circle on the plane, the radius of that circle is 12