Question

In triangle $ABC,BD$ is a median. $CF$ intersects $BD$ at $E$ so that $\overline{BE}=\overline{ED}$. Point $F$ is on $AB$. Then, if $\overline{BF}=4,\overline{BA}$ equals.

• A. $10$
• B. $12$
• C. $15$
• D. $20$
• E. None of these

Answer 1

The correct option is B $12$

$Given:BDismedianof△ABC;CFintersectBDatE;$

$\overline{BE}=\overline{ED},\overline{BF}=4$

$Tofind:\overline{BA}$

$Solution:FromD,drawalineparalleltoCFintersectingABatG.$

$In△AFC$

$AD=DC$

$\therefore Gismid-pointofAF\left(Bymidpointthm\right)$

$\therefore AG=FG-\left(1\right)$

$In△BDG$

$BE=ED$

$\therefore Fismid-pointofBG\left(Bymidpointthm\right)$

$\therefore BF=FG-\left(2\right)$

$\therefore AG=FG=BF$

$\&AB=BF+FG+AG=3BF$

$⟹AB=3\left(4\right)=12$