SOLUTION: Two parallel chords on opposite sides of the centre of a circle are 9 cm apart. If the chords are 8 cm and 12 cm long, then what is the radius of the circle?

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Question 765504: Two parallel chords on opposite sides of the centre of a circle are 9 cm apart. If the chords are 8 cm and 12 cm long, then what is the radius of the circle?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Two parallel chords on opposite sides of the centre of a circle are 9 cm apart. If the chords are 8 cm and 12 cm long, then what is the radius of the circle?
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I don't have the means to draw the sketch, but I can try to describe it to you. I am working with two right triangles. Both triangles have the radius as the hypotenuse with a known leg=1/2 of the length of the respective chords (4 and 6 cm). The sum of the unknown legs=distance(9cm) between the given chords.
r=radius
..
sqrt%28r%5E2-4%5E2%29%2Bsqrt%28r%5E2-6%5E2%29=9
sqrt%28r%5E2-4%5E2%29=9-sqrt%28r%5E2-6%5E2%29
square both sides
r%5E2-16=81-18%2Asqrt%28r%5E2-36%29%2Br%5E2-36
18%2Asqrt%28r%5E2-36%29=61
sqrt%28r%5E2-36%29=61%2F18
square both sides again
r^2-36=11.48
r^2=36+11.48=47.48
r=√47.48
r=6.89 cm