Please help me.

**owningbro1** · November 6th 2008, 06:35 PM

A circular garbage can is wedged into a rectangular corner. the can has a diameter of 48cm. Find the exact distance from the corner point to the can (PA).

P=corner
A=the point of the outer part of the circle
PA is the segment connecting this
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**earboth** · November 7th 2008, 01:36 AM

Originally Posted by owningbro1

A circular garbage can is wedged into a rectangular corner. the can has a diameter of 48cm. Find the exact distance from the corner point to the can (PA).

P=corner
A=the point of the outer part of the circle
PA is the segment connecting this

I've attached a sketch of the situation.

I assume that the distance PA = x. If so:

The radii and the 2 walls form a square with its side length = r.

x + r = diagonal d of the square.

Use Pythagorean theorem to calculate the diagonal:

$d = r \cdot \sqrt{2}$

$x = d - r = r \cdot \sqrt{2} - r = r\left( \sqrt{2} - 1\right)$

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