# Three identical cirular arcs inside a circle

**Example**

Circular arcs of radii 10 cm are described inside a circle of radius 10 cm. The centers of each arc are on the circle and so arranged so that they are equally distant from each other. Find the area enclosed by three arcs shown as shaded regions in the figure.

**Solution**

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$A_1 = \frac{1}{6}\pi (10^2) - \frac{1}{2}(10^2) \sin 60^\circ$

$A_1 = 9.06 \, \text{ cm}^2$

$A_{required} = 6A_1 = 6(9.06)$

$A_{required} = 54.35 \, \text{ cm}^2$ *answer*