Odd Theorems and Geometric Anomalies

First: Construct a Reuleaux Triangle.  Show that the area of this triangle is
(where S is the radius of the arcs that make up the shape).
Next, Have a look at each of the following fun theorems.  Pick your favorite one of these and demonstrate that it is true by illustrating it with a dimensioned drawing.
Demonstrate the Pitot Theorem
Demonstrate this “Odd” Theorem
Demonstrate Miquel’s Theorem
Demonstrate the Simpson Line
Demonstrate Archimedes Twin Circles
Demonstrate this theorem

Save the drawing as “geomlab_yourlastname.dwg”

Turn in a printout of your drawings.