MathDB
Internal Bisector

Source: 0

April 23, 2009
geometryangle bisectorsimilar triangles

Problem Statement

In triangle ABC ABC, internal bisector of angle A A intersects with BC BC at D D. Let E E be a point on [CB \left[CB\right. such that \left|DE\right|\equal{}\left|DB\right|\plus{}\left|BE\right|. The circle through A A, D D, E E intersects AB AB at F F, again. If \left|BE\right|\equal{}\left|AC\right|\equal{}7, \left|AD\right|\equal{}2\sqrt{7} and \left|AB\right|\equal{}5, then ∣BF∣ \left|BF\right| is
<spanclass=′latex−bold′>(A)</span> 755<spanclass=′latex−bold′>(B)</span> 7<spanclass=′latex−bold′>(C)</span> 22<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> 10<span class='latex-bold'>(A)</span>\ \frac {7\sqrt {5} }{5} \qquad<span class='latex-bold'>(B)</span>\ \sqrt {7} \qquad<span class='latex-bold'>(C)</span>\ 2\sqrt {2} \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ \sqrt {10}
Back to ProblemsView on AoPS