Circle chord

Calculate the length of the chord of the circle with radius r = 10 cm, length of which is equal to the distance from the center of the circle.

Result

x =  8.944 cm

Solution:

r2=x2+(x/2)2 r2=x2+x2/4 r2=5/4⋅x2 x=2r/5 x=8.944 cmr^2 = x^2+(x/2)^2 \ \\ r^2 = x^2+x^2/4 \ \\ r^2 = 5/4 \cdot x^2 \ \\ x = 2r / \sqrt5 \ \\ x = 8.944 \ \text{cm}

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