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P25 [Geometry] - Turkish NMO 1st Round - 2004

Source:

November 12, 2013
geometryangle bisector

Problem Statement

Let DD be the foot of the internal angle bisector of the angle AA of a triangle ABCABC. Let EE be a point on side [AC][AC] such that CE=CD|CE|= |CD| and AE=65|AE|=6\sqrt 5; let FF be a point on the ray [AB[AB such that DB=BF|DB|=|BF| and AB<AF=85|AB|<|AF| = 8\sqrt 5. What is AD|AD|?
<spanclass=latexbold>(A)</span> 105<spanclass=latexbold>(B)</span> 8<spanclass=latexbold>(C)</span> 415<spanclass=latexbold>(D)</span> 75<spanclass=latexbold>(E)</span> None of above <span class='latex-bold'>(A)</span>\ 10\sqrt 5 \qquad<span class='latex-bold'>(B)</span>\ 8 \qquad<span class='latex-bold'>(C)</span>\ 4\sqrt{15} \qquad<span class='latex-bold'>(D)</span>\ 7\sqrt 5 \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}