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In the diagram, O is the center of a circle with radii OP=OQ=5. What is the perimeter of the shaded region?

 

 Feb 19, 2022
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The perimeter of the shaded region is  \(10+\text{arc}(QP)\). The circumference of the entire circle is \(10\pi\). The arc is \(1 \over 6\) of the total perimeter, meaning that the arc's length is \({5 \over 3}\pi\). Thus, the perimeter is \(\color{brown}\boxed{10+{5 \over3}\pi}\)

 Feb 19, 2022

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