Question 858267
<pre>
She hasn't learned how to draw on here yet.

{{{drawing(200,200,-14,14,-14,14,
green(line(-5,0,12,0),locate(2.8,2,17)),

circle(0,0,0.25),circle(0,0,0.23),circle(0,0,0.11),circle(0,0,0.09),circle(0,0,0.07),circle(0,0,0.05),circle(0,0,0.03),circle(0,0,0.01),

locate(-5.5,14,A),locate(-5.5,-12,B),locate(12.5,6,C),locate(12.5,-5,D),

locate(0,0,O),locate(-7.4,.4,24),locate(9.5,0.5,10),

circle(0,0,13), line(12,-5,12,5), line(-5,12,-5,-12) )}}}

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.

{{{drawing(200,200,-14,14,-14,14,

circle(0,0,0.3),circle(0,0,0.25),circle(0,0,0.14),circle(0,0,0.09),circle(0,0,0.18),circle(0,0,0.05),circle(0,0,0.03),circle(0,0,0.01),
locate(-7.4,6,12), locate(-2.5,0,x), locate(6,0,y),
locate(-5.5,14,A),locate(-5.5,-12,B),locate(12.5,6,C),locate(12.5,-5,D),
green(line(-5,0,12,0)),locate(-6.4,.4,E),locate(10.5,0,F),locate(10.5,3,5),
locate(0,0,O),red(line(0,0,-5,12),line(0,0,12,5)),

locate(-1.8,6.8,r),locate(5.5,5,r),

circle(0,0,13), line(12,-5,12,5), line(-5,12,-5,-12) )}}}

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</pre>