How to Draw Tangent Circles using Cones

Solving the Problem of Apollonius with Conic Sections

This video describes a non-standard way of finding tangent circles to a given set of 3 circles, known as the Problem of Apollonius. It uses conic sections rather than straightedge and compass. I feel this approach is more intuitive and gives a better understanding of the problem.

To try out the custom Geogebra tools described at the end of the video, check out
https://www.geogebra.org/m/hpffzp9b

#SoME1
This is my entry into The Summer of Math Exposition (SoME1) contest created by 3blue1brown. The goal of the contest is to encourage more people to put out math explainers online
https://3b1b.co/some1

#geogebra
Visualizations and demonstration done using Geogebra
https://www.geogebra.org/

Inspiration for this came from reading
http://jwilson.coe.uga.edu/EMAT6680Fa...
I wanted to know why the center of the tangent circles always lie on a conic section, regardless of the configuration of the circles. Even the parabola can be seen as a limiting case, where one circle has radius zero (a point) and one circle has infinite radius (a line).