3 Unit A2 1: Pure Mathematics (A-level only)
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Question 138
Figure 1 below shows the sector OAB OAB\,OAB of a circle. The chord AB AB\,AB divides the sector into a triangle and a shaded segment.
The angle AOB AOB\,AOB is π6\displaystyle \frac{\pi}{6}6π radians and the radius of the sector is 106 10\sqrt{6}\,106 m.
Show that the area of the shaded segment is
k(π−3)k(\pi - 3)k(π−3) m2^22
where k k\,k is an integer to be found.