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? Can you please explain

Click here to see ALL problems on Pythagorean-theorem

Question 772824: 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? Can you please explain EVERY step in detail? Thanks so much!
Answer by ankor@dixie-net.com(22740) (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?
:
Draw a diagram of this this,
r = the distance from the center to the ends of both Chords.
Let x = the distance from the center to the middle of the 8 cm chord
then
(9-x) = the distance from the center to the middle of the 12 cm chord:
:
A right triangle formed with the 8 cm chord, using pythag
r^2 = 4^2 + x^2
Another right triangle formed with the 12 cm chord
r^2 = 6^2 + (9-x)^2
:
r^2 = r^2, we can write the equation
6^2 + (9-x)^2 = 4^2 + x^2
36 + 81 - 18x + x^2 = 16 + x^2
117 - 18x + x^2 = 16 + x^2
subtract x^2 from both sides
117 - 18x = 16
117 - 16 = 18x
101x = 18x
x = 101/18
x = 5.611
:
Use the 8 cm chord right triangle to find r
r^2 = 4^2 + 5.611^2
r^2 = 16 + 31.48
r =
r = 6.89 cm is the radius
:
Check this on the 12 cm chord right triangle
9 - 5.611 = 3.39, the dist from the center to the chord
r^2 = 6^2 + 3.39^2
r^2 = 36 + 11.48
r^2 = 47.48
r =
r = 6.89 cm confirms our solution for the radius