Solutions 45511

Two parallel chords in a circle with a radius of 6 cm have lengths of 6 cm and 10 cm. Calculate their distance from each other. Find both solutions.

Correct answer:

x =  8.5128 cm
y =  1.8795 cm

Step-by-step explanation:

$$\begin{gathered} r=6\text{cm} \\ a=6\text{cm} \\ b=10\text{cm} \\ {r}^2=x_1^2+(a/2{)}^2 \\ {x}_1=\sqrt{r^2-(a/2{)}^2}=\sqrt{6^2-(6/2{)}^2}=3\sqrt{3}\text{cm}\doteq 5.1962\text{cm} \\ {r}^2=x_2^2+(b/2{)}^2 \\ {x}_2=\sqrt{r^2-(b/2{)}^2}=\sqrt{6^2-(10/2{)}^2}=\sqrt{11}\text{cm}\doteq 3.3166\text{cm} \\ x=x_1+x_2=5.1962+3.3166=8.5128\text{cm} \end{gathered}$$

$y=|x_1-x_2|=|5.1962-3.3166|=1.8795\text{cm}$

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