Circle's chords

In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle.

Correct answer:

r =  17.6163 cm

Step-by-step explanation:

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

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