MathDB
P17 [Geometry] - Turkish NMO 1st Round - 2013

Source:

April 16, 2013
geometryarea of a triangle

Problem Statement

Let ABCABC be an equilateral triangle with side length 1010 and PP be a point inside the triangle such that PA2+PB2+PC2=128|PA|^2+ |PB|^2 + |PC|^2 = 128. What is the area of a triangle with side lengths PA,PB,PC|PA|,|PB|,|PC|?
<spanclass=latexbold>(A)</span> 63<spanclass=latexbold>(B)</span> 73<spanclass=latexbold>(C)</span> 83<spanclass=latexbold>(D)</span> 93<spanclass=latexbold>(E)</span> 103 <span class='latex-bold'>(A)</span>\ 6\sqrt 3 \qquad<span class='latex-bold'>(B)</span>\ 7 \sqrt 3 \qquad<span class='latex-bold'>(C)</span>\ 8 \sqrt 3 \qquad<span class='latex-bold'>(D)</span>\ 9 \sqrt 3 \qquad<span class='latex-bold'>(E)</span>\ 10 \sqrt 3