How do I find correct spot on triangle to draw circle so all three sides of the triangle touch the circle?

I would like to find the spot on the face of the triangle so that when I’m sizing the circle the circle will fill the triangle so all three sides of the triangle touch the circle at once.

I have tried different things, including google. But I’m probably making it harder then it should be or simple don’t know the correct terms to search for.

Here are some stupid things I have been trying.

Do you want the circle to remain a circle or is it acceptable if the shape is different? It’s easy enough if the triangle is equilateral because a circle centered in the triangle will touch all three edges. If it’s not equilateral, you can find the point to draw a circle. For example, on a triangle similar to yours you could do this.

Yes I want it to remain a circle and it’s not equilateral.

Looking at your image I’m not sure how you got all your points for the dotted line that is not on the green axes. So I looked some more on google and found this. Is this how you did it or I’m I still making it to complicated?


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With a little practice, you can use the Offset tool to find the center:


Draw two guides halving two of the angles. The centerpoint is at their intersection.


The guideline at an angle was placed with the Protractor tool.

Bisecting two of the angles as Anssi suggests will give you the center, too. That would be the center of the circle. You can do a no-measure method of finding the bisector of a couple of angles using the Arc tool.


This seems to work too.



I think however, due to the segmentation of the circles you will need just the right number of segments to actually hit all three sides bang on a vertex.


…or use the Pie tool found in Arc’s…


From grade school geometry: bisect the interior angles, that will locate the center point of a circle tangent to all three sides of any triangle, equilateral, obtuse or acute. Sister Ethel Rita taught me that one about half a century ago. But the offset tool is a super quick way to find the interior angle bisector.

Cool thread - I’ve been refreshing my geometry from 35 years ago & learning some useful SU tricks!

Only in catholic school would you have learned geometry in grade school. I was speaking French in second grade. :slight_smile: