Center Circle in Pentagon

[mjs1138 (Mike Sullivan)]

I have a design that I need to center a circle inside a pentagon. However when I use “select circle, select pentagon then click the center tool I get what is in the picture. It certainly doesn’t look like it’s centered. Thoughts?

[JessN (Jess)]

Have you used the measure tool to confirm the distances between the inner and outer shape? I believe LB is centering correctly. Mine doesn’t look centered either, yet it is the same distance between top/bottom.

[thelmuth (Tim Helmuth)]

It is centered. The centering tool uses the bounding box for the pentagon shape. See my screenshot below. I drew a rectangle that just fits the pentagon (blue) andcentered the circle to it. You see it’s the same as using the pentagon to center. If you want equal spacing from the edges, that takes a bit more work.

[thelmuth (Tim Helmuth)]

Note the original dimension of your circle. Increase the circle to fill the pentagon and just touch all sides.

Then, with the anchor point set to center resize the circle to it’s original dimension.

This is NOT centered in the pentagon, but it is spaced evenly from the edges, which is what I believe you’re after.

[mjs1138 (Mike Sullivan)]

Thanks. This is what I need.

[ClayJar (Nathaniel Klumb)]

@thelmuth

This is NOT centered in the pentagon, but it is spaced evenly from the edges, which is what I believe you’re after.

Pardon my pedantry, but the circle is centered in the pentagon given your steps, but the geometric center of the pentagon (or any regular polygon of an odd number of sides) is not at the center of its rectangular bounding box.

I’ve occasionally used an alternate method of drawing a 2N-sided polygon (in another color/layer) along with my N-sided polygon, grouping them. The center of the 2N polygon is at the center of the bounding box, so the centering tools work. I then just turn off the 2N polygon when I’m done designing.

Then again, I also just use simple-to-me trig functions to calculate precise placements, so math is apparently my jam.

[DBat (Dennis E Batterman)]

That is centered to the points of the pentagon, but not to the sides.I believe

[ClayJar (Nathaniel Klumb)]

If it’s a regular polygon, there isn’t a difference, yes? If it’s not a regular polygon, “center” becomes ambiguous and requires more precise definitions.

For triangles, the centroid, circumcenter, incenter and orthocenter are all well-known centers, and for certain triangles, the orthocenter may even be outside the triangle. At some point I just drop the math and go with “Well, that looks decent.”