Let △ A B C be a triangle with angle bisector CL ( L ∈ A B ) and median CM ( M ∈ A B ). I should find LM if B C = a , A C = b , A B = c ( a &gt; b ).

Question

Let   △  A  B  C be a triangle with angle bisector CL   (  L  ∈  A  B  ) and median CM   (  M  ∈  A  B  ). I should find LM if   B  C  =  a  ,  A  C  =  b  ,  A  B  =  c  (  a  &amp;gt;  b  ).

Matteo Kirk · Accepted Answer

Step 1Since             A      L              L      B        =      b    a    , we obtain:   A  L  =            b      c              a      +      b       and   L  M  =  A  M  −  A  L  =      c    2    −            b      c              a      +      b        =            c      (      a      −      b      )              2      (      a      +      b      )        .Step 2We can get AL by the following way:            A      L              c      −      A      L        =      b    a              c      −      A      L              A      L        =      a    b        c          A      L        −  1  =      a    b        c          A      L        =  1  +      a    b        c          A      L        =            a      +      b        b              A      L        c    =      b          a      +      b        A  L  =            b      c              a      +      b        .

Let triangle ABC be a triangle with angle bisector CL (L in AB) and median CM (M in AB). I should find LM if BC=a, AC=b, AB=c(a>b).

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