Let $C _ { 1 } , C _ { 2 }$ be two circles of equal radii $R$. If $C _ { 1 }$ passes through the centre of $C _ { 2 }$ prove that the area of the region common to them is $\frac { R ^ { 2 } } { 6 } ( 4 \pi - \sqrt { 27 } )$.
Let $C _ { 1 } , C _ { 2 }$ be two circles of equal radii $R$. If $C _ { 1 }$ passes through the centre of $C _ { 2 }$ prove that the area of the region common to them is $\frac { R ^ { 2 } } { 6 } ( 4 \pi - \sqrt { 27 } )$.