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

2. 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:

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

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