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Hosam
Lv 6
Hosam asked in Science & MathematicsMathematics · 7 years ago

Find the radius of the circle of intersection between the two spheres ...?

First sphere centered at (1,1,1) and has a radius of 10

Second sphere centered at (5, 7, 13) and has a radius of 8.

2 Answers

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  • ?
    Lv 4
    4 years ago

    Sphere Sphere Intersection

    Source(s): https://shorte.im/a90SW
  • Pope
    Lv 7
    7 years ago

    Let the centers be A(1, 1, 1) and B(5, 7, 13), and let P be any point of intersection.

    In triangle ABP,

    AB = 14

    BP = 8,

    PA = 10

    area(ABP) = 16√(6) ... by Heron's formula

    Let Q be the foot of the altitude from P.

    area(ABP) = (AB)(PQ)/2

    (14)PQ/2 = 16√(6)

    PQ = 16√(6)/7

    radius of circle of intersection = 16√(6)/7

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