You have to prove that BE:EX =3:1
2 years, 4 months ago
Just construct DF parallel to BX . So by MPT in BXC. DF = 1/2 BX. Now DF // EX. So by MPT in triangle ADF. We get XE = 1/2 DF. i.e. XE = 1/4 BX and so BE:EX = 3:1
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Nice solution :).
yeah but we can also do it by the use of mid point theorem , just draw a line parallel to BC through point E.and further you can solve
If you apply Menelaus' theorem twice you will get that ratio.
can we do it by applying mid point theorem?
I do not see how it could be helpful in this case.
draw a line parallel to BC through the point E. say PQ,then in triangle ABD, E is mid point of AD and also,EP parallel to BD,therefore AP=BP,and similarly AQ=QC.Now Triangle BXC is similar to Triangle EXQ,
Therefore,BX/EX=XC/XQ=BC/EQ.Let us take,BX/EX=BC/EQ,i.e BX/EX=BC/1/2DC,
i.e BX/EX=BC/1/2(1/2B/C),That gives,BX/EX=4/1,
Now subtracting 1 from both sides,that gives,
I think Actually we can prove this by 3 ways.
I am glad you have found your answers. As always in math, there are many ways to do things.
Yeah thank you.
You have Given that BD=CD and AE=DE.