From a chord to an overlap
8 written marks
A circle of radius \(8\) cm has chord \(AB=8\sqrt3\) cm. Its centre is \(O\).
Part a · 3 marks
Find the minor angle \(AOB\) and the perpendicular distance from \(O\) to \(AB\).
Part b · 2 marks
Find the area of the minor segment.
Part c · 3 marks
A second circle of radius \(8\) cm has centre \(O_2\) on the opposite side of \(AB\), with \(OO_2=8\) cm, and passes through \(A,B\). Find the area and perimeter of the common region.
Complete-answer checking, worked solutions and indicative written criteria.
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