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!

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> 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!      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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?
------------
The product of the segments of the chord = product of the segments of the diameter.
--------------
3*3 = (r-2)*(r+2) = r^2 - 4
r+=+sqrt%2813%29
----------------
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) About Me  (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