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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Akash Deep
·
2 years, 1 month ago

@Karthik Venkata
–
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
–
Chinmay Sangawadekar
·
2 years, 1 month ago

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If you apply Menelaus' theorem twice you will get that ratio.
–
Maria Kozlowska
·
2 years, 1 month ago

@Maria Kozlowska
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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,
BE:EX=3:1

I think Actually we can prove this by 3 ways.
–
Chinmay Sangawadekar
·
2 years, 1 month ago

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@Chinmay Sangawadekar
–
I am glad you have found your answers. As always in math, there are many ways to do things.
–
Maria Kozlowska
·
2 years, 1 month ago

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TopNewestJust 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 – Akash Deep · 2 years, 1 month ago

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– Karthik Venkata · 2 years, 1 month ago

Nice solution :).Log in to reply

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– Chinmay Sangawadekar · 2 years, 1 month ago

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 solveLog in to reply

If you apply Menelaus' theorem twice you will get that ratio. – Maria Kozlowska · 2 years, 1 month ago

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– Chinmay Sangawadekar · 2 years, 1 month ago

can we do it by applying mid point theorem?Log in to reply

– Maria Kozlowska · 2 years, 1 month ago

I do not see how it could be helpful in this case.Log in to reply

BE:EX=3:1I think Actually we can prove this by 3 ways.– Chinmay Sangawadekar · 2 years, 1 month agoLog in to reply

– Maria Kozlowska · 2 years, 1 month ago

I am glad you have found your answers. As always in math, there are many ways to do things.Log in to reply

– Chinmay Sangawadekar · 2 years, 1 month ago

Yeah thank you.Log in to reply

You have Given that BD=CD and AE=DE. – Chinmay Sangawadekar · 2 years, 1 month ago

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