Circle's chords

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

Final 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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