Creating accurate circular arcs with shape editor tool

I'm curious as to how I can create accurate 90° arcs, using the shape editor. Actually this is just a single exercise in a broader attempt to understand how the curve handles relate to their point handles.

To evaluate the precise relationship between the two in a 90° arc, I did the following:

• Window > Snap to grid
• Drew a circle of radius 100 pixels, with center point at 200, 200.
• Cleared the circle's fill.
• Drew vertical and horizontal lines exactly through the circle's center.
• Used those lines to slice (Ctrl+4) the circle into exact quarters.
• Colored the lower right corner arc red.
• Selected the red arc, and activated the shape editor tool.
• Selected the bottom point handle, to reveal the curve handle.
• Looking at the info bar, I can see that the curve handle is both 1) horizontal with, and 2) 55.2 pixels to the right of the point handle.

What significance does the (55.2% x radius) have? I've looked through the help in both Web Designer 5 and Xtreme 5, hoping to develop a quality understanding of bezier curves, but there doesn't seem to be quite enough information (for me).

By the way, the example attached was actually done in Web Designer, but the process for both applications is identical ... and I'm certain that this group is more knowledgeable.

If any of you have light to share, I would appreciate reading your words. Thanks.

See attached graphic.
Saludos,
Bob.

Thanks for your input, Bob.

Your proceedure is included in what I described in my first post, above. I have no problem slicing the circle into quarters. :)

I'm curious about the relationship between a curve's the point handle and its curve handle (particularly when creating primatives using the shape editor tool).

Here is your answer... http://www.cgafaq.info/wiki/Bezier_Circle

Thanks for that reference, Ampa. That would make the more precise length of the handle (55.2284749830794% x radius) ... for what it's worth (given a very slight margin of error). :cool:

I found a very informative presentation of material, specific to the [approximate] bézier construction of a quarter circle here, and here.

Hmm ... I woke up this morning with a realization about sliced circles (arcs). Given the graphic example in the opening post of this thread, once a circle is sliced into pieces, it must be treated as a bezier curve (since it sports manipulation handles), and NOT (no longer) a radiused arc.

An accurate realization Curtis. ;):)