SOLUTION: Pleas help me to solve this question: AB and CD are two parallel chords of a circle. If AB = 24 cm, CD = 10 cm and distance between these chords is 17 cm, find the radius of the ci

Algebra ->  Circles -> SOLUTION: Pleas help me to solve this question: AB and CD are two parallel chords of a circle. If AB = 24 cm, CD = 10 cm and distance between these chords is 17 cm, find the radius of the ci      Log On


   

Question 858267: Pleas help me to solve this question: AB and CD are two parallel chords of a circle. If AB = 24 cm, CD = 10 cm and distance between these chords is 17 cm, find the radius of the circle.
Found 2 solutions by Seutip, Edwin McCravy:
Answer by Seutip(231) About Me  (Show Source):
You can put this solution on YOUR website!
Hello there! ;)
http://jwilson.coe.uga.edu/emt725/ParallelChords/ParallelChords.html

Click on the link, I'm sorry it's hard to explain things when I can't draw. :)

Hope it still helps somehow!

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
She hasn't learned how to draw on here yet.



Draw EF through O perpendicular to AB and CD,
also draw radii OA and OC.  EF is the perpendicular
bisector of the chords, so that AE=12 and CF=5.
Label the radii r and label OE and OF as x and y, 
respectively.



Using the Pythagorean theorem on the two right triangles OEA and OFC

x² + 12² = r²
 y² + 5² = r²

Simplify and subtract the two equations:

  x²  + 144 = r²
  y²  +  25 = r²
----------------
x²-y² + 119 = 0

      x²-y² = -119
 Factor the left side:

 (x-y)(x+y) = -119

We are given that EF = 17 = x+y, so
we can substitute 17 for (x+y)

  (x-y)(17) = -119

Divide both sides by 17

        x-y = -7 , add that equation to
        x+y = 17
      -----------
       2x   = 10
          x = 5

Substitute in x+y = 17 and get y  = 12.

Substitute in

      y²+25 = r²
     12²+25 = r²
     144+25 = r²
        169 = r²
         13 = r

Answer: the radius is 13 cm. 

Edwin