A tangent enclosure
8 written marks
Tangents at \(A\) and \(B\) to a circle with centre \(O\) meet at \(T\). The radius is \(6\) cm and the minor angle \(AOB\) is \(\displaystyle \frac{2\pi}{3}\). The shaded gap is enclosed by \(TA\), \(TB\) and the minor arc \(AB\).
Part a · 3 marks
Find \(AT\) and \(OT\) exactly.
Part b · 3 marks
Find the exact area of the shaded gap.
Part c · 2 marks
Find the exact perimeter of the shaded gap.
Complete-answer checking, worked solutions and indicative written criteria.
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