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Geometry Level pending

In triangle $ABC$ , point $D$ is the midpoint of $BC$ . $BE$ meets $AC$ at $E$ , and Segment $BE$ and $AD$ intersect at point $F$ . Knowing that $AF: FD$ is $1:5$ , what is $AE: EC$ ?

1/10 1/4 1/8 1/6

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Alexis Yang
Mar 8, 2016

Draw line FX that is parallel to BC. Extend line BE and draw line AY that intersects with the extended line that is parallel to BC.

Using the Side-Splitting theorem of similar triangles, we can find the ratios of several segments. AF:FD=1:5, BD:BC=1:2, AX:AB=1:6, XF:BD=1:6 so XF:BC=1:12, XF:AY=5:6, XF:BC/XF:AY=1:12/5:6, AY:BC=1:10, AE:EC=1:10

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