Carpentry and Woodworking - How do I cut this out of plywood?

I'm trying to make a training aid for my golf game. Lame I know, but I know I can do it much cheaper than I can buy one.

Something similar to this:
http://perfectgolfswingreview.net/PlaneBoardHandArc.jpg

I've tried making one out of PVC pipe, there are several commercial products out there like it, but they have somehow got professionally molded pipe to make their perfect circle. Like this:
http://www.pvcsports.com/images/full%20circle%20swing%20trainer.jpg

I can't seem to accomplish that, so I'm wondering about this plywood board option.

My main question is, how would I trace a quarter circle that big, perfectly round, into a piece of plywood and then join the two pieces together to get that nice perfect half circle.

Are there special measurements to making a quarter circle?

A string a nail, and a pencil. The nail goes in the center. The string's length equals the radius. You draw the circle with the pencil keeping the string taught. If the arc of the circle is larger then the board then the pivot/nail is placed outside the board to draw a circle whose arc equals the arc you want on the board.

String and nail will also help guide your jig saw.

Is that so you can practice maintaining body angle?

The PVC one might be easy. Take a look at a coil of black plastic irrigation pipe, also used for wells.

Bud