Two arcs and a clockwise journey
8 written marks
The minor and major arcs between \(A\) and \(B\) on a circle are in the ratio \(2:7\). The minor arc has length \(\displaystyle \frac{8\pi}{3}\) cm. Take the radius \(OA\) as direction zero.
Part a · 2 marks
Find the minor and reflex central angles.
Part b · 3 marks
Find the radius and the area of the minor sector.
Part c · 3 marks
From \(A\), a point travels clockwise along the major arc to \(B\) and then completes two further clockwise revolutions. Find its total distance and its final direction measured anticlockwise in \([0,2\pi)\).
Complete-answer checking, worked solutions and indicative written criteria.
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