Circles

In the circle with a radius, 7.5 cm is constructed of two parallel chords whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions, write both).

Final Answer:

x =  10.5 cm
y =  1.5 cm

Step-by-step explanation:

$$\begin{gathered} r=7.5\text{cm} \\ {t}_1=9\text{cm} \\ {t}_2=12\text{cm} \\ {r}^2=x_1^2+(t_1/2{)}^2 \\ {r}^2=x_2^2+(t_2/2{)}^2 \\ {x}_1=\sqrt{r^2-(t_1/2{)}^2}=\sqrt{7.5^2-(9/2{)}^2}=6\text{cm} \\ {x}_2=\sqrt{r^2-(t_2/2{)}^2}=\sqrt{7.5^2-(12/2{)}^2}=\frac{9}{2}=4.5\text{cm} \\ x=x_1+x_2=6+4.5=10.5\text{cm} \end{gathered}$$

$y=|x_1-x_2|=|6-4.5|=1.5\text{cm}$

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