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 cm A=60  B=A/2=60/2=30  r=D/2=8/2=4 cm  r2=r2+t22 r t cosB t2=2 r t cosB t=2 r cosB=2 r cos30 =2 4 cos30 =2 4 0.866025=6.928 cmD=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}



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