Question 624289
A chord 6 cm long is 2 cm from the center of a circle. How long is a chord that is 1 cm from the center of the same circle?
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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