perplexus.info :: Shapes : Sphere intersection

Sphere intersection (Posted on 2024-10-04)

Sphere (x+2)²+(y+3)²+(z+2)²=25 and (x+2)²+(y+3)²+(z-4)²=16 intersect at a circle.

What is the radius of this circle of contact?

No Solution Yet Submitted by Danish Ahmed Khan

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Simpler solution

Comment 3 of 3 |

The spheres are 6 units apart. The triangle containing the centers of the spheres and the edge of the circle has lengths 4-5-6. The radius of the circle is the height to the side of length 6.

By Heron's formula the triangle has area 15sqrt(7)/4 and so the radius is 5sqrt(7)/4/

Posted by Jer on 2024-10-09 07:35:48

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