Circle annulus

There are two concentric circles in the figure. The chord of the larger circle, 10 cm long, is tangent to the smaller circle. What does annulus have?

Correct answer:

S =  78.5398 cm²

Step-by-step explanation:

$$\begin{gathered} t=10\text{cm} \\ {R}^2=(t/2{)}^2+r^2 \\ {R}^2-r^2=(t/2{)}^2 \\ S=\pi \cdot R^2-\pi \cdot r^2 \\ S=\pi \cdot (R^2-r^2) \\ S=\pi \cdot (t/2{)}^2=3.1416\cdot (10/2{)}^2=78.5398{\text{cm}}^2 \end{gathered}$$

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