Circle chord

What is the length x of the chord circle of diameter 115 m, if the distance from the center circle is 11 m?

Result

x =  112.876 m

Solution:

D=115 m t=11 m  r=D/2=115/2=1152=57.5 m   (x/2)2+t2=r2  (x/2)2=r2t2  x=2 r2t2=2 57.5211212741112.876112.876 mD=115 \ \text{m} \ \\ t=11 \ \text{m} \ \\ \ \\ r=D/2=115/2=\dfrac{ 115 }{ 2 }=57.5 \ \text{m} \ \\ \ \\ \ \\ (x/2)^2 +t^2=r^2 \ \\ \ \\ (x/2)^2=r^2 - t^2 \ \\ \ \\ x=2 \cdot \ \sqrt{ r^2-t^2 }=2 \cdot \ \sqrt{ 57.5^2-11^2 } \doteq \sqrt{ 12741 } \doteq 112.876 \doteq 112.876 \ \text{m}



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