Two chords

In a circle with a radius of 8.5 cm, two parallel chords are constructed, the lengths of which are 9 cm and 12 cm. Find the distance of the chords in a circle.

Correct answer:

x =  13.2319 cm
y =  1.1903 cm

Step-by-step explanation:

$$\begin{gathered} r=8.5\text{cm} \\ a=9\text{cm} \\ b=12\text{cm} \\ {r}^2=x_1^2+(a/2{)}^2 \\ {x}_1=\sqrt{r^2-(a/2{)}^2}=\sqrt{8.5^2-(9/2{)}^2}=2\sqrt{13}\text{cm}\doteq 7.2111\text{cm} \\ {r}^2=x_2^2+(b/2{)}^2 \\ {x}_2=\sqrt{r^2-(b/2{)}^2}=\sqrt{8.5^2-(12/2{)}^2}\doteq 6.0208\text{cm} \\ x=x_1+x_2=7.2111+6.0208=13.2319\text{cm} \end{gathered}$$

$y=|x_1-x_2|=|7.2111-6.0208|=1.1903\text{cm}$

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