We will present 3 proofs of this result, all based on Circles: a Mathematical View, by Dan Pedoe, Dover Publications, 1979.
Well, why are there many biographies of Abraham Lincoln? Each proof illuminates the relationships among the parts of the triangle and various parts of geometry. That is, each proof gives you a different view of the subject. The mere statement of a theorem is like a flat statement that Lincoln was the 16th president. We want to know more than that.