How to Prove the Area Inequality Between Excenters and Triangle ABC?

Harmeet Singh
If I1,I2,I3 are the excentres of tringle ABC then prove that
Area of triangle I1 I2 I3 >=4*Area of triangle ABC ?
 
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What have you done? atleast did you get an idea from where can we reach the answer or even couldn't start with. specify them
 

Thread 'Find the polar form of a complex number'

The working out suggests first equating ## \sqrt{i} = x + iy ## and suggests that squaring and equating real and imaginary parts of both sides results in ## \sqrt{i} = \pm (1+i)/ \sqrt{2} ## Squaring both sides results in: $$ i = (x + iy)^2 $$ $$ i = x^2 + 2ixy -y^2 $$ equating real parts gives $$ x^2 - y^2 = 0 $$ $$ (x+y)(x-y) = 0 $$ $$ x = \pm y $$ equating imaginary parts gives: $$ i = 2ixy $$ $$ 2xy = 1 $$ I'm not really sure how to proceed from here.
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