Concentric circles and chord

In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord?

Correct answer:

r₂ =  4 cm

Step-by-step explanation:

$$\begin{gathered} d=10\text{ cm } \\ t=6\text{ cm } \\ {r}_1=d\mathrm{/}2=10\mathrm{/}2=5\text{ cm } \\ {r}_1^2=r_2^2+(t\mathrm{/}2{)}^2 \\ {r}_2=\sqrt{r_1^2-(t\mathrm{/}2{)}^2}=\sqrt{5^2-(6\mathrm{/}2{)}^2}=4\text{ cm} \end{gathered}$$

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