# Circled Corners

Three circles have been drawn at the vertices of this triangle. What is the area of the inner shaded area?

## Problem

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?

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## Student Solutions

The three angles of the triangle add to $180^{\circ}$, so the combined area of the three sectors of the circles that are inside the triangle add up to half a circle with area:

$\frac{1}{2} \times \pi \times 2^2 = \frac {4\pi}{2}= 2\pi$.

So the grey area is $(80- 2\pi) cm^2$.

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