Drawing and arranging circles and triangles

Okay, there is an amusement which requires arranging 10 name brand disposable cups in a triangle.

Dimensions are:


We’ll round up to 93mm for the overall dimension:

We need one circle above and one below lined up and touching:

Since the basic arrangement is a hexagon we have to start by rotating things 30 degrees to get them into the initial position:

Duplicate and drag the duplicate into alignment with the original and then rotate by 60 degrees:

repeat until one has a full set:

Next, fill in the points by duplicating a set:

dragging the center circle into alignment with a circle adjacent to the position which needs to be filled:

and rotating and then deleting the redundant circles:

Repeat for the other points:

Select the three circles at the points and duplicate them and increase their dimension by some reasonable amount (say 25mm):

Note that it will be relocated, so it will be necessary to rotate each circle so that a node is at the top, then drag the misplaced resized circle into alignment with the original, then reposition it by half the distance which it is larger:

358.591 + 12.5 == 371.091

Repeat for the other two points:

Select each circle, duplicate it and resize it to a suitable size to secure the cup at a reasonable height — 76.5mm seems reasonable, but this should be verified be sourcing a cup, measuring it, and then doing a test cut. Note that when resize the circles will again reposition:

drag each circle back so that it is encompassed by the original:

then use the align tool to center it within the original:

then delete the originals repeating as need be:

Then rotate the top circle 60 degrees and draw a polyline which connects the tangents of the larger circles at the points:

Do a Boolean Union of those circles and the polyline:


roundedtriangleand10circles.c2d (194.4 KB)

Working out joinery and toolpaths is left as an exercise for the reader.


An alternate way to draw the rounded triangle would be to draw a triangle/polyline which had its points on the centers of the 3 circles and then offset the path to the outside by the desired radius.