Two chords

From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords.

Final Answer:

t =  6.9282 cm

Step-by-step explanation:

$$\begin{gathered} D=8\text{cm} \\ A=60{}^{\circ } \\ B=A/2=60/2=30{}^{\circ } \\ r=D/2=8/2=4\text{cm} \\ {r}^2=r^2+t^2-2\cdot r\cdot t\cdot \cos B \\ {t}^2=2\cdot r\cdot t\cdot \cos B \\ t=2\cdot r\cdot \cos B=2\cdot r\cdot \cos 30°=2\cdot 4\cdot \cos 30°=2\cdot 4\cdot 0.866025=6.928=6.9282\text{cm} \end{gathered}$$

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