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The diagram shows a triangle and three circles whose centres are at the vertices of the triangle. The area of the triangle is $80 cm^2$ and each of the circles has radius $2cm$. What is the area, in $cm^2$, of the shaded area?

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

*This problem is taken from the UKMT Mathematical Challenges.*