How computers can help with maths

One of my viewers asked me the following question: "Let ABCD be an isosceles trapezoid with (AB parallel to CD). Let E be the mid-point of AC. Denote by omega and ohm the circumcircles of triangles ABE and CDE, respectively. Let P be the crossing point of the tangent to omega at A with the tangent to ohm at D. Prove that PE is tangent to ohm." I couldn't think of a proof using classical (synthetic) geometry, so decided to use analytic geometry, and the algebra got a bit messy so I used a computer algebra system (SageMath) to help out. So this video is just a little intro to using computers to help out with maths. I also go off on a tangent about problem-solving techniques and how to come up with a strategy for geometry proofs. You can try out SageMath (without installing) at: http://sagecell.sagemath.org Or install SageMath: http://www.sagemath.org/download.html For linux, it says "At the moment there are no distribution-specific packages available. Progress is being made for Debian and Fedora." but I think that's out of date because I installed it on Ubuntu with "sudo apt install sagemath". SageMath tutorial: https://doc.sagemath.org/html/en/tutorial/ MetaPost tutorials: https://www.tug.org/metapost.html Installing metapost is usually done by installing TeX Live https://www.tug.org/texlive/ or MikTeX https://miktex.org/ MetaPost source code for the diagram: https://github.com/jennigorham/metapost-examples/blob/master/isosceles-trapezoid.mp