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TT2008 Junior O-Level - P3

Source:

September 4, 2010
geometryperimetergeometry proposed

Problem Statement

Acute triangle A1A2A3A_1A_2A_3 is inscribed in a circle of radius 22. Prove that one can choose points B1,B2,B3B_1, B_2, B_3 on the arcs A1A2,A2A3,A3A1A_1A_2, A_2A_3, A_3A_1 respectively, such that the numerical value of the area of the hexagon A1B1A2B2A3B3A_1B_1A_2B_2A_3B_3 is equal to the numerical value of the perimeter of the triangle A1A2A3.A_1A_2A_3.
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