# Wood Pile Perimeter

Weekly Problem 30 - 2011

Three touching circles have an interesting area between them...

Three touching circles have an interesting area between them...

## Problem

Image

The diagram shows three touching circles each of radius $5$cm and a line which touches two of them.

Find, in terms of $\pi$, the total perimeter of the two shaded shapes.

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

## Student Solutions

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The straight part is the same length as two radii, so is $10\text{cm}$ long.

The perimeter of the shaded shapes is therefore $10+10\pi\text{cm}$.