SOLUTION: AB and CD ARE TWO PARALLEL CHORDS OF A CIRCLE WHICH ARE ON EITHER SIDE OF THE CENTRE. SUCH THAT AB=10cm AND CD=24cm FIND THE RADIUS IF THE DISTANCE BETWEEN AB AND CD IS 17cm.

Draw the two red radii:



This splits the green line, which is 17cm in two parts,
x and y, so



and we solve it for y:



The green line splits the two chords, which are 10cm
and 24cm, in half, 5cm and 12cm:

And we have two right triangles.  We use the Pythagorean theorem on
both right triangles:

 and 

So

 and 





And since 









Substitute in













So the radius of the circle is 13.

Edwin