MathDB

23

Part of 2005 Postal Coaching

Problems(1)

Another incircle

Source: Indian Postal Coaching 2005

10/27/2005
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.
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