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# Balls in the corner

## Question

A big ball (of diam 7 ft) just touches three walls, and a little ball touches three walls and the big ball. What's the diameter of the little ball?

Assume that the balls are spheres and therefore only touch at a single point.

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If the big and little balls are touching the same walls and the floor counts as one of the walls (if the big ball has the little ball "trapped" inside the corner of a rectangle), then the first objective is to find length of the vacant diagonal left from the big ball. The midpoint of the big ball acts as the corner of a cube, each length being 3.5 feet. The diagonal of that cube is sqrt(3)*3.5, and subtracting the radius of the big ball leaves a line of approximately 2.562... feet in length.

The ratio of the diagonal from the corner to the outer edge of the big ball compared to the vacant length in the corner should be equal to the ratio of the diagonal from the corner to the outer edge of the small ball compared to the vacant length in the corner it does not take up. Once we know the length of the vacant diagonal left from the little ball, we can subtract that from the length of the vacant diagonal left from the big ball which will leave us with the diameter of the little ball.

= 1.875644...

...I think...

Edited by BobbyGo
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I'm thinking one of the walls must be the floor.

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No ceiling .. and the big ball also touches the small ball.

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I meant the ceiling as a wall. of course they are on the floor too

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