Can you relate it to area of triangle?

Geometry Level 4

If P P be any interior point of the equilateral triangle A B C ABC of side length 2 units and also x a , x b , x c { x }_{ a },{ x }_{ b },{ x }_{ c } be the distances of P from the sides B C , C A BC,CA and A B AB respectively. Compute x a + x b + x c { x }_{ a }+{ x }_{ b } + {x }_{ c } .

None of these choices 3 4 \cfrac { \sqrt { 3 } }{ 4 } 3 \sqrt { 3 } 2 3 2\sqrt { 3 } 3 2 \cfrac { \sqrt { 3 } }{ 2 }

Sahil Bansal by Sahil Bansal , 21, India

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1 solution

In an equilateral triangle x a + x b + x c = a l t i t u d e = 3 2 ∗ 2 = 3 . x_a+x_b+x_c=altitude=\dfrac {\sqrt3}2 *2=\sqrt3.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Exactly, a direct application of viviani's theorem

Aditya Kumar - 5 years, 3 months ago

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