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Alteration to the message 16262

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  • Milton Donaire Peña
    Thanks to Javier Garcia Capitán for his observations to the problems that I have raised, and also to Pavan Naidu, for his observations. Forgive the correct
    Message 1 of 2 , Apr 9, 2008
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      Thanks to Javier Garcia Capitán for his observations to the problems
      that I have raised, and also to Pavan Naidu, for his observations.


      Forgive the correct terms of reference of the problem:

      in A Triángle ABC, P is on AC,C1: circle inscript in ABC y C2:
      circle inscript in BPC. The straight line parallel to AC and tangent
      to the circumference C2 felling AB and to BP in X and Y. C3: circle
      inscript in XBY, The other one straight line parallel to AC and
      tangent to the circumference C3 ¿is too tangent to the circumference
      C1? Since I solve it?
    • Nikolaos Dergiades
      Dear Milton, It is sufficient to prove that r2 + r3 = r . . . (1) where r2, r3, r are the inradii of triangles BPC, BXY, ABC If r1 is the inradius of triangle
      Message 2 of 2 , Apr 10, 2008
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        Dear Milton,
        It is sufficient to prove that r2 + r3 = r . . . (1)
        where r2, r3, r are the inradii of triangles BPC, BXY, ABC
        If r1 is the inradius of triangle BAP
        BP=z, AP=x, PC=y and S is the double area of ABC then
        (1) is equivalent to
        Stewart's equality . . aax + ccy = zz(x+y) + xy(x+y)
        since
        r1 = xS/(x+y)(x+z+c)
        r2 = yS/(x+y)(y+z+a)
        r3 = r1(h_b-2r2)/h_b
        where h_b = S/(x+y) is the B_altitude and
        r = S/(a+c+x+y)
        It would be nice to have a synthetic proof.
        Best regards
        Nikos Dergiades


        >
        > in A Triángle ABC, P is on AC,C1: circle inscript in ABC y
        > C2:
        > circle inscript in BPC. The straight line parallel to AC
        > and tangent
        > to the circumference C2 felling AB and to BP in X and Y.
        > C3: circle
        > inscript in XBY, The other one straight line parallel to AC
        > and
        > tangent to the circumference C3 ¿is too tangent to the
        > circumference
        > C1? Since I solve it?
        >
        >
        >
        > ------------------------------------
        >
        > Yahoo! Groups Links
        >
        >
        >


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