Law of Cotangents

One of those ridiculously beuatiful geometry facts that you wonder how you never knew. As often, saw it at the Futility Closet, Inscribe an equilateral triangle in a rectangle, or rectiscribe a rectangle around an equilateral triangle so that they share a vertex. Then the other triangles in the rectangle have a beautiful relationship. Originally from Tom Apostol and Mamikon Mnatsaka. But wait! This is just a special case of what can only be called the Law of Cotangents. Click the checkbox and you won't believe what they said next!
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