How can I make the opposite of Reuleaux triangle?

A Reuleaux triangle:

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What I’m trying to make, is the opposite of that, meaning the lines bend inward to looks something like:

enter image description here

I achieved that by making three circles, but it’s a pain to align the third circle properly.

I’m sure that there’s an easier way to make a shape like this. (geometrically)


It’s pretty easy to make this with a 4 sided (diamond)
Just lay out four circles in a box (smart guides make it take a second) and cut out the center.

Answer

Here are 2 ways:

    • Make a circle
    • Duplicate the circle so it touches the other
    • Rotate the newly created circle around the first one by 60 degrees (alt to click to trigger numeric input and copy).

    enter image description here

    Image 1: Animation of first method

    • Draw a same sided triangle
    • Draw a circle with radius of half the length of triangle edge (or diameter of edge).
    • Copy a circle at each triangle vertex.

Then use shape builder to remove the excess.

For the super pedantic

Now somebody brought up that this wont be perfect. And they are right. Bézier splines can not make a perfect circle so even though it would be mathematically super accurate there’s no way I can use a 3 segment Bézier to be super pedantically accurate. However, I can construct a more accurate approximate circle with for example jooGraphFunction that is made out of 12 segments (instead of 4) then it will be perfect within limits of floating point precision. This also makes cloning trivial since you have a control point at each intersections so just drag the point to point and be done with it.

Attribution
Source : Link , Question Author : WELZ , Answer Author : Ovaryraptor

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