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# geometry

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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

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 $$\color{brown}\boxed{10+{5 \over3}\pi}$$