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For 6 cm chord: one leg of right triangle=3 cm (1/2 chord) other leg of right triangle=2 cm from center hypotenuse=radius=√(3^2+2^2)=√13 .. For chord =x one leg of right triangle=x/2 (1/2 chord) other leg of right triangle=1 cm from center hypotenuse=radius=√(x/2)^2+1^2) .. √(x/2)^2+1^2)=√13 (x/2)^2+1^2=13 x^2/4+1=13 x^2+4=52 x^2=48 x=√48 x≈6.93 cm
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