game of areas in right triangle May Olympiad (Olimpiada de Mayo) 2016 L2 P5
Source:
September 25, 2021
gamecombinatoricsgeometryareaswinning strategy
Problem Statement
Rosa and Sara play with a triangle , right at . Rosa begins by marking two interior points of the hypotenuse , then Sara marks an interior point of the hypotenuse different from those of Rosa. Then, from these three points the perpendiculars to the sides and are drawn, forming the following figure.
https://cdn.artofproblemsolving.com/attachments/9/9/c964bbacc4a5960bee170865cc43902410e504.png
Sara wins if the area of the shaded surface is equal to the area of the unshaded surface, in other case wins Rosa. Determine who of the two has a winning strategy.