Geometric Puzzle Magnificence

Here is yet another collection of beautiful geometric problems from Catriona Agg (née Shearer).  For some reason I found these a bit more challenging than the previous ones.   Some of them required more time to “see” the breakthrough.

See Geometric Puzzle Magnificence (revised)

(Update 11/13/2022)  Problem #3 Solution Corrected Simon Ellis and his sister Mary pointed out that my solution had assumed what I wanted to prove (implicitly), so I had to come up with a new solution.  I have added it to a revised article.