Two chords 2

The length of one of two chords of a circle is 12cm. If the chords are 6cm and 7cm, respectively, away from the center of the circle, calculate the length of the second chord.

Correct answer:

b =  9.5917 cm

Step-by-step explanation:

$$\begin{gathered} a=12\text{cm} \\ {x}_1=6\text{cm} \\ {x}_2=7\text{cm} \\ {r}^2=(a/2{)}^2+x_1^2 \\ {r}^2=(b/2{)}^2+x_2^2 \\ (a/2{)}^2+x_1^2=(b/2{)}^2+x_2^2 \\ b=2\cdot \sqrt{(a/2{)}^2+x_1^2-x_2^2}=2\cdot \sqrt{(12/2{)}^2+6^2-7^2}=2\sqrt{23}\doteq 9.5917\text{cm} \\ \text{ Verifying Solution: } \\ r=\sqrt{(a/2{)}^2+x_1^2}=\sqrt{(12/2{)}^2+6^2}=6\sqrt{2}\text{cm}\doteq 8.4853\text{cm} \\ {r}_2=\sqrt{(b/2{)}^2+x_2^2}=\sqrt{(9.5917/2{)}^2+7^2}=6\sqrt{2}\text{cm}\doteq 8.4853\text{cm} \\ r=r_2 \end{gathered}$$

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