1982 USAMO Problems/Problem 5

Problem

$A,B$ , and $C$ are three interior points of a sphere $S$ such that $AB$ and $AC$ are perpendicular to the diameter of $S$ through $A$ , and so that two spheres can be constructed through $A$ , $B$ , and $C$ which are both tangent to $S$ . Prove that the sum of their radii is equal to the radius of $S$ .

Solution

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1982 USAMO (Problems • Resources)
Preceded by Problem 4	Followed by Last Question
1 • 2 • 3 • 4 • 5
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1982 USAMO Problems/Problem 5

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