Menelaus Theorem :

If a tranversal is drawn cutting through the three sides of a triangle, the sides of the triangle are divided in a definite ratio.
 

Machine Input :

Point Order : ABCDEF
Hypotheses : coll(ABF) coll(CDB) coll(AEC) coll(EDF)
Conjecture : DC/DB FB/FA EA/EC = 1
 

Machine Output :


We can equivalently prove that :-

1.0(DC/DB)(FB/FA)
--------------------------   =  1
1.0(EC/EA)

Proof:

   1.0(DC/DB)(FB/FA)
   ---------------------
   1.0(EC/EA)

      By putting (FB/FA) = [EDB]/[EDA]

   1.0(DC/DB)[EDB]
=  ---------------------
   1.0(EC/EA)[EDA]

      By putting (EC/EA) = [EDC]/[EDA]

   1.0(DC/DB)[EDB]
=  ---------------------
   1.0[EDC]

      By putting [EDC] = [EDB](DC/DB)

   1.0
=  ---------------------
   1.0

Compute Time=0.263 seconds