2026 IGCSE Additional Mathematics February/March 0606/22 Q5

The diagram shows a design for a badge.

\(ABC\) is an equilateral triangle with side \(x\text{ cm}\).

The arcs \(BC\), \(CA\) and \(AB\) are parts of the circles with centres \(A\), \(B\) and \(C\) respectively.

1. Write down the size of angle \(ABC\) in radians.
   Give your answer in terms of \(\pi\).[1]
2. The area of the badge is \(2(\pi-\sqrt3)\text{ cm}^2\).
   Find \(x\).[5]