Wood pile perimeter

Weekly Problem 30 - 2011
Three touching circles have an interesting area between them...
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

Image
Wood Pile Perimeter



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.