Please tell me the answer of question 2. I am in need.
Janardon Adhikary , 5 Years ago
Grade 10
Analytical Geometry> Please tell me the answer of question 2. ...
1 Answers
Aditya Gupta
Last Activity: 5 Years ago
ok so first off lets understand the meaning of mean proportional. if c is a mean proportional between a and b, then c^2= ab. it is basically the same as geometric mean.
that means ED^2= AE*AD. let AE= a and ED= b then b^2= a(a+b) or b/a= 1+(a/b)= k (say)
now, NBF is similar to NED by AA criterion (as sides of parallelogram are parallel and transversal properties).
so NB/NE= BF/ED but BF=AE (opposite sides of parallelogram are equal)
or NB/NE= a/b or NE= (b/a)*NB= kNB
also MED is similar to MBC by AA.
so ME/MB= ED/BC= b/(a+b) or MB= (1+a/b)ME= kME
now, NE= NB+BE and MB= ME+BE so that NE – MB= NB – ME
we substitute NE and MB from above
kNB – kME=NB – ME
or k(NB – ME)= NB – ME
or (NB – ME)(k – 1)=0
obviously k cannot be 1 else a=b which would imply k=1+1/1= 2. since 1 cannont be equal to 2, hence k is not 1.
so, cancelling k – 1 both sides
NB – ME= 0
or NB= ME
kindly approve :)
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