# How to place a perfect curve to join two circles together?

I have two circles in this position

I'm looking to acheive this (but more perfect with the flow of the curve meeting the circle perfectly on the right) notice, that it is slightly off)

How would I be able to do this that the three curves when whole are perfect circles?

I am using Corel Draw, but can also do this in Illustrator.

Sizes of the circles and positioning

• In your picture with the 3 circles, why not trace over the connecting curve with the pen tool? May 1, 2017 at 14:47
• Why is a circle connecting perfect? I mean its only a C1 continuous connection, C2 is easily attainable and surely more perfect. May 1, 2017 at 15:40

## 1 Answer

Measure the radi/diameters of your circles.

1. Decide on a radius(diameter for the connecting curve, the higher this value the less curved the connection is.
2. Draw a circle with the desired diameter + the diameter (or 2 * radius) of the upper circle, centered on the upper circle center.
3. Draw a circle with the desired diameter - the diameter (or 2 * radius) of the lower circle, centered on the lower circle center.

4. The center of the new circle is at the intersection point of these 2 circles with the radius you decided in step 1.

• a triumph of intuitive math.
– user82991
May 1, 2017 at 21:51
• @user287001 Geometry is intuitive if you have insight into it. But its a bit problematic to use effectively. I have 30 years of geometry studies behind me so what is self eveident to me is not necceserily self exident to everybody. You may wish to see this lecture's start Where the limitation is explained well. May 2, 2017 at 6:44
• Good to note: the desired radius should be at least larger than `d - 2*r1 - 2*r2`, where `d` is the distance between the centers of the two circles. Otherwise the connecting curve is not able to connect the two circles. Jan 3, 2022 at 8:38