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Question Number 36314 by behi83417@gmail.com last updated on 31/May/18

Commented by behi83417@gmail.com last updated on 31/May/18

$B D = m e d i a n, B E = a n g u l a r b i s e c t o r$ $E F ∥ B D$ $B F = ? (i n t e r m o f A \overset{▴}{B C} s i d e s)$ $s p i c i a l c a s e : A B - A C = d (= c o n s t .)$
	Answered by ajfour last updated on 31/May/18

	$L e t B F = q, D E = p$ $\frac{q}{a} = \frac{p}{b / 2} & \frac{\frac{b}{2} - p}{\frac{b}{2} + p} = \frac{a}{c}$ $\Rightarrow \frac{b}{2} - p = \frac{a b}{a + c}$ $q = \frac{2 a}{b} (\frac{b}{2} - \frac{a b}{a + c})$ $o r q = a - \frac{2 a^{2}}{a + c} = \frac{a (c - a)}{c + a} .$
	Commented by behi83417@gmail.com last updated on 31/May/18

	$g o o d j o b d e a r A j f o u r! t h a n k s .$
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