Exact area and perimeter of the region between a tangent, a line through the centre and a minor arc
Exact area and perimeter of the region between a tangent, a line through the centre and a minor arc
IB Year 6 | Grade 12
6 marks
In the diagram below, \(O\) is the centre of a circle. The line \(AB\) touches the circle at \(A\), where \(AB=6\text{ cm}\) and \(OB=4\sqrt3\text{ cm}\). The line segment \(OB\) cuts the circle at \(C\). The shaded region is bounded by \(AB\), \(BC\) and the minor arc \(AC\).
- Find the exact area of the shaded region.[4]
- Find the exact perimeter of the shaded region.[2]
Solution:
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Answer:(a) \(6\sqrt3-2\pi\text{ cm}^2\) (b) \(6+2\sqrt3+\dfrac{2\sqrt3\,\pi}{3}\text{ cm}\)
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