Challenge Problems!

The problems here appear to be stated in geometric terms but the solutions will typically require algebraic and analytic methods moreso than the methods of classical geometry known to Euclid and the ancient Greeks. These problems are intended to stimulate your problem solving skills or, if nothing more, provide some harmless diversion and mental exercise. ENJOY!

Problem 1 (Medium Level of Difficulty)

Problem 2 (Medium Level of Difficulty)

Problem 3 (High Level of Difficulty)