Homework Help: Geometry

Posted by Chica on Thursday, May 19, 2011 at 11:09pm.

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?

A. 8cm
B. 10cm
C. 12cm
D. 13cm

Could please shed some light on how this problem is worked out.

Geometry - Reiny, Friday, May 20, 2011 at 8:39am
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^2= 144
x = 12

Since the chord is diameter of the circle on the plane, the radius of that circle is 12

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