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## Distance and Spheres | AIME I, 1987 | Question 2

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1987 based on Distance and Spheres.

## Distance and Sphere – AIME I, 1987

What is the largest possible distance between two points, one on the sphere of radius 19 with center (-2,-10,5) and the other on the sphere of radius 87 with center (12,8,-16)?

• is 107
• is 137
• is 840
• cannot be determined from the given information

### Key Concepts

Angles

Algebra

Spheres

AIME I, 1987, Question 2

Geometry Vol I to Vol IV by Hall and Stevens

## Try with Hints

The distance between the center of the spheres is $\sqrt{(12-(-2)^{2}+(8-(-10))^{2}+(-16-5)^{2}}$

=$\sqrt{14^{2}+18^{2}+21^{2}}$=31

The largest possible distance=sum of the two radii+distance between the centers=19+87+31=137.