SOLUTION: 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?
Thank you in advance!
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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?
Thank you in advance!
Found 2 solutions by Alan3354, lwsshak3:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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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The product of the segments of the chord = product of the segments of the diameter.
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3*3 = (r-2)*(r+2) = r^2 - 4
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c^2 = (r-1)*(r+1) = r^2 - 1 = 12
c^2 = 2sqrt(3) =~ 3.464
chord = 2c
chord = 6.928 cm
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
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?
**
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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