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 has the concentric circle while touching this chord?

Correct answer:

r₂ =  4 cm

Step-by-step explanation:

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

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