Chord

In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord?

Correct result:

t =  107.3 cm

Solution:

$$\begin{gathered} r=60 \\ t=4x \\ {r}^2=x^2+(t\mathrm{/}2{)}^2 \\ {r}^2=x^2+(4x\mathrm{/}2{)}^2 \\ x=r\mathrm{/}\sqrt{1+4^2\mathrm{/}4}=60\mathrm{/}\sqrt{1+4^2\mathrm{/}4}=12\sqrt{5}\doteq 26.8328 \\ t=4\cdot x=4\cdot 26.8328=48\sqrt{5}=107.3\text{ cm} \end{gathered}$$

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