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Problem 206
206
In the diagram, ABC is a semicircle with diameter AC, centre O and radius 6 cm. The length of the arc AB is 15 cm. The point X lies on AC and BX is perpendicular to AX.
Find the perimeter of the shaded region BXC.
Solution
First, find the angle \\ \angle AOB \\ using the arc length formula: \\ \text{Arc length} = r \theta \\ where \\ r = 6 \\ and \\ \text{Arc length} = 15. \\ Thus, \\ \theta = \frac{15}{6} = 2.5 \\text{ radians}.
