Two chords 6

A chord PQ is 10.4cm long, and its distance from the center of a circle is 3.7cm. Calculate the length of a second chord RS, which is 4.1cm from the center of this circle.

Correct answer:

t₂ =  9.7816 cm

Step-by-step explanation:

$$\begin{gathered} t_1=10.4\text{cm} \\ {x}_1=3.7\text{cm} \\ {x}_2=4.1\text{cm} \\ {r}^2=x_1^2+(t_1/2{)}^2 \\ r=\sqrt{x_1^2+(t_1/2{)}^2}=\sqrt{3.7^2+(10.4/2{)}^2}\doteq 6.382\text{cm} \\ {r}^2=x_2^2+(t_2/2{)}^2 \\ {t}_2=2\cdot \sqrt{r^2-x_2^2}=2\cdot \sqrt{6.382^2-4.1^2}=9.7816\text{cm} \end{gathered}$$

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