MathDB
Another incircle

Source: Indian Postal Coaching 2005

October 27, 2005
geometrygeometry unsolved

Problem Statement

Let Γ\Gamma be the incircle of an equilateral triangle ABCABC of side length 22 units. (a) Show that for all points PP on Γ\Gamma, PA2+PB2+PC2=5PA^2 +PB^2 +PC^2 = 5. (b) Show that for all points PP on Γ\Gamma, it is possible to construct a triangle of sides equal to PA,PB,PCPA,PB,PC and whose area is equal to 34\frac{\sqrt{3}}{4} units.
Back to ProblemsView on AoPS