Chord

In a circle with radius r = 60 cm, there is a chord that is 4 times longer than its distance from the centre. What is the length of the chord?

Final Answer:

t =  107.3 cm

Step-by-step explanation:

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

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