Circle's chords

The circle has two chord lengths, 30 and 34 cm. The shorter one is from the center twice as a longer chord. Determine the radius of the circle.

Correct answer:

r =  17.6163 cm

Step-by-step explanation:

$$\begin{gathered} t_1=30 \\ {t}_2=34 \\ {r}^2=(t_1/2{)}^2+(2x{)}^2 \\ {r}^2=(t_2/2{)}^2+x^2 \\ 3x^2=(t_2/2{)}^2-(t_1/2{)}^2 \\ x=\sqrt{((t_2/2{)}^2-(t_1/2{)}^2)/3}=\sqrt{((34/2{)}^2-(30/2{)}^2)/3}\doteq 4.6188 \\ {r}_1=\sqrt{(t_1/2{)}^2+(2x{)}^2}=\sqrt{(30/2{)}^2+(2\cdot 4.6188{)}^2}\doteq 17.6163 \\ {r}_2=\sqrt{(t_2/2{)}^2+(x{)}^2}=\sqrt{(34/2{)}^2+4.6188^2}\doteq 17.6163 \\ r=r_1=17.6163=17.6163\text{cm} \end{gathered}$$

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