D is the midpoint of side BC of triangle ABC and E is the midpoint of AD BE produced - Maths - Triangles

Question

D is the midpoint of side BC of triangle ABC and E is the midpoint
of AD BE produced meets AC at point F prove that BE: BF = 3:4

Mayank Jha · Accepted Answer

Dear stduent,

Let us draw the figure

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_57bed12b8af90%20png"
style="width: 326px; height: 170px;">
Let's take point G on segment AC such that DG||BF
As D is the midpoint of BC, by converse of midpoint theorem, FG = GCApplying midpoint theorem in triangle CDG, BF = 2DG
As E is a midpoint of AD and EF||DG, AF = FGApplying midpoint theorem in triangle DAC, DG = 2EFBEBF=BF - EFBF =2DG -DG2 2DG =3DG2*2 DG=34

Regards

D is the midpoint of side BC of triangle ABC and E is the midpoint of AD. BE produced meets AC at point F . prove that BE: BF = 3:4