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tangents to the incircle

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  • pneagoe
    Dear Hyacinthos, Let ABC be a triangle, P a point inside and A1, A2 the intersection points of the line AP with the incircle (the point A1 is on the segment
    Message 1 of 4 , Mar 4, 2007
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      Dear Hyacinthos,

      Let ABC be a triangle, P a point inside and A1, A2
      the intersection points of the line AP with the incircle
      (the point A1 is on the segment AA2).
      A' is the intersection point of the tangent to the incircle
      at A1 with the line BC and A" is the intersection point of
      the tangent to the incircle at A2 with the line BC.
      Similarly define B', B", C', C".
      Prove that A', B', C' are collinear points (on the line L)
      and AA", BB", CC" are concurrent lines (at the point Q).

      If the point R is the tripol of the line L then prove that
      the points P, Q, R are collinear points.

      Best regards,
      Petrisor Neagoe
    • pneagoe
      I m sorry! R is the pol of a line L with respect to the incircle. Best regards, Petrisor Neagoe
      Message 2 of 4 , Mar 4, 2007
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        I'm sorry!
        R is the pol of a line L with respect to the incircle.

        Best regards,
        Petrisor Neagoe

        --- In Hyacinthos@yahoogroups.com, "pneagoe" <pneagoe@...> wrote:
        >
        > Dear Hyacinthos,
        >
        > Let ABC be a triangle, P a point inside and A1, A2
        > the intersection points of the line AP with the incircle
        > (the point A1 is on the segment AA2).
        > A' is the intersection point of the tangent to the incircle
        > at A1 with the line BC and A" is the intersection point of
        > the tangent to the incircle at A2 with the line BC.
        > Similarly define B', B", C', C".
        > Prove that A', B', C' are collinear points (on the line L)
        > and AA", BB", CC" are concurrent lines (at the point Q).
        >
        > If the point R is the tripol of the line L then prove that
        > the points P, Q, R are collinear points.
        >
        > Best regards,
        > Petrisor Neagoe
        >
      • pneagoe
        Sorry, my english is bad! R is the pole of the line L with respect to the incircle. Petrisor Neagoe
        Message 3 of 4 , Mar 4, 2007
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          Sorry, my english is bad!
          R is the pole of the line L with respect to the incircle.

          Petrisor Neagoe

          --- In Hyacinthos@yahoogroups.com, "pneagoe" <pneagoe@...> wrote:
          >
          >
          > I'm sorry!
          > R is the pol of a line L with respect to the incircle.
          >
          > Best regards,
          > Petrisor Neagoe
          >
          > --- In Hyacinthos@yahoogroups.com, "pneagoe" <pneagoe@> wrote:
          > >
          > > Dear Hyacinthos,
          > >
          > > Let ABC be a triangle, P a point inside and A1, A2
          > > the intersection points of the line AP with the incircle
          > > (the point A1 is on the segment AA2).
          > > A' is the intersection point of the tangent to the incircle
          > > at A1 with the line BC and A" is the intersection point of
          > > the tangent to the incircle at A2 with the line BC.
          > > Similarly define B', B", C', C".
          > > Prove that A', B', C' are collinear points (on the line L)
          > > and AA", BB", CC" are concurrent lines (at the point Q).
          > >
          > > If the point R is the tripol of the line L then prove that
          > > the points P, Q, R are collinear points.
          > >
          > > Best regards,
          > > Petrisor Neagoe
          > >
          >
        • pneagoe
          Dear Hyacinthos, Let ABC be a triangle, P a point inside and A1, A2 the intersection points of the line AP with the incircle (the point A1 is on the segment
          Message 4 of 4 , Mar 4, 2007
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            Dear Hyacinthos,

            Let ABC be a triangle, P a point inside and A1, A2
            the intersection points of the line AP with the incircle
            (the point A1 is on the segment AA2).
            A' is the intersection point of the tangent to the incircle
            at A1 with the line BC and A" is the intersection point of
            the tangent to the incircle at A2 with the line BC.
            Similarly define B', B", C', C".
            Prove that A', B', C' are collinear points (on the line L)
            and AA", BB", CC" are concurrent lines (at the point Q).

            The point Q is the tripole of the line L.
            If the point R is the pole of the line L with respect to the
            incircle then prove that the points P, Q, R are collinear.

            Best regards,
            Petrisor Neagoe
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