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SMO 2007 Open Round 1 Question 17

SMO · SMO 2007 Open Round 1

Question 17

In triangle $ABC$, $AC\gt AB$. The internal angle bisector of $A$ meets $BC$ at $D$, and $E$ is the perpendicular foot from $B$ onto $AD$. Suppose $AB=5$, $BE=4$, $AE=3$. Find $\dfrac{AC+AB}{AC-AB}\,ED$.