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# circle

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The figure shows two concentric circles. If the length of chord AB is 100 units and chord AB is tangent to the smaller circle, what is the area of the shaded region? Express your answer in terms of pi.

Dec 5, 2020

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The figure shows two concentric circles. If the length of chord AB is 100 units and chord AB is tangent to the smaller circle, what is the area of the shaded region? Express your answer in terms of pi.

Hello Guest!

$$R^2=50^2+r^2\\ R^2-r^2=50^2\\ R^2-r^2=2500$$

$$A=\pi R^2-\pi r^2\\ A=(R^2-r^2) \pi \\ \color{blue}A=2500 \pi\ square\ units$$

Dec 5, 2020