Concentric circles

In the circle with diameter 19 cm is constructed chord 9 cm long. Calculate the radius of a concentric circle that touches this chord.

Correct answer:

r =  8.3666 cm

Step-by-step explanation:

$$\begin{gathered} (19\mathrm{/}2{)}^2=r^2+(9\mathrm{/}2{)}^2 \\ r=\sqrt{(19\mathrm{/}2{)}^2-(9\mathrm{/}2{)}^2}=8.3666\text{ cm} \end{gathered}$$

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