# 05 Three identical cirular arcs inside a circle

**Example 05**

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 05**

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

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

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

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

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