[AD] How to connect a line between the outer edges of two circles (external tangents to two unequal circles)

[Anonymous Puddle]

When you have two circles and you would like to draw two lines connecting the outer edges of Circle 1 to Circle 2, you need to know where on the curve of each circle to connect each point of the lines to. Technically, we are seeking to find the external tangents to two unequal circles.

Here is the expected result:

At first, after converting the circles from shapes to curves, I thought the solution was to simply take the topmost (and bottom-most) node of each circle and draw a line between them. The problem is that the points where the line needs to connect on each circle will almost never be the top- or bottom-most or point of the circle, due to the difference in the sizes of the circles and their positioning. See the red shape in the image and recording below.

Thankfully, there is way! Some math is required to achieve a precise result, and all credit goes to this YouTube video (of which I have no affiliation). Since Affinity is a different type of software than the one shown in the video and there is no Compass Tool in Affinity, you will need to create circles in each step in the video instead but it is certainly possible in Affinity Designer. I've included an Affinity Designer file that contains all of the steps in the video so you can see how it is achieved with Designer. Pay close attention to the options at the bottom of the screen when using the Ellipse Tool (see image below), as this will be necessary to achieve proper results.

If you need me to elaborate step-by-step on how I adapted the YouTube tutorial to work with the tools in Designer, I would be happy to explain further in a separate post.

Please note: if the two circles are equal size, I believe there is a different method required than the one utilized here.

External tangent line between two unequal cricles.afdesign

[GarryP]

People might also be interested in these threads which show various techniques that can be used in similar situations: