Circle annulus

There are 2 concentric circles in the figure. Chord of larger circle 10 cm long is tangent to the smaller circle. What are does annulus have?

Correct result:

S =  78.5398 cm²

Solution:

$$\begin{gathered} R^2=(10\mathrm{/}2{)}^2+r^2 \\ {R}^2-r^2=5^2 \\ S=\pi \cdot R^2-\pi \cdot r^2 \\ S=\pi \cdot (R^2-r^2) \\ S=\pi \cdot 5^2=3.1416\cdot 5^2=78.5398{\text{cm}}^2 \end{gathered}$$

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