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# Tangent question, please explain

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Two circles are drawn, with the same center. A chord of the large circle is drawn, so that it is tangent to the small circle. If the chord has a length of  then find the area of the ring-shaped region that is inside the large circle but outside the small circle.

Jun 10, 2020

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Two circles are drawn, with the same center. A chord of the large circle is drawn, so that it is tangent to the small circle.

If the chord has a length of 12 then find the area of the ring-shaped region that is inside the large circle but outside the small circle.

$$\begin{array}{|rcll|} \hline \mathbf{R^2} &=& \mathbf{6^2 + r^2} \\ \mathbf{R^2 - r^2} &=& \mathbf{36} \\ \hline \end{array}$$

$$\begin{array}{|rcll|} \hline \mathbf{\text{area of the ring}} &=& \mathbf{\pi R^2 - \pi r^2} \\ \text{area of the ring} &=& \pi (R^2 - r^2) \quad | \quad \mathbf{R^2 - r^2=36} \\ \mathbf{\text{area of the ring}} &=& \mathbf{36\pi} \\ \hline \end{array}$$

Jun 10, 2020