# 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.

Correct result:

t =  6.928 cm

#### Solution:

$D=8 \ \text{cm} \ \\ A=60 \ ^\circ \ \\ B=A/2=60/2=30 \ ^\circ \ \\ r=D/2=8/2=4 \ \text{cm} \ \\ \ \\ r^2=r^2 + t^2 - 2 \cdot \ r \cdot \ t \cdot \ \cos B \ \\ t^2=2 \cdot \ r \cdot \ t \cdot \ \cos B \ \\ t=2 \cdot \ r \cdot \ \cos B ^\circ =2 \cdot \ r \cdot \ \cos 30^\circ \ =2 \cdot \ 4 \cdot \ \cos 30^\circ \ =2 \cdot \ 4 \cdot \ 0.866025=6.928 \ \text{cm}$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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