Question 872351
If one side of a parallelogram inscribed in a circle of radius 5cm is 6cm then other side is?
<pre>
A parallelogram inscribed in a circle is always a rectangle.

I'll assume you have proved that using the fact that equal chords
subtend equal arcs:

{{{drawing(400,400,-6,6,-6,6, circle(0,0,5), locate(3.2,-2,x), 
red(line(0,0,3,0)), locate(1.5,0,3cm), locate(3.2,2,x),
green(line(0,0,3,4)), locate(0,4,6cm),locate(1.5,2,5cm),
rectangle(-3,-4,3,4) )}}}

We know that the green line is 5cm because it is a radius.
We know that the red line is 3cm because it is half-way across
the rectangle which has side 6cm.

The answer will be the rectangle's height or 2x.

We find x by the Pythagorean theorem:

3² + x² = 5²
 9 + x² = 25
     x² = 16
      x = 4cm

So the rectangle's height is 2x or 8cm.

Edwin</pre>