## tangents to the incircle

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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
Message 1 of 4 , Mar 4, 2007
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
• 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
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
>
• 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
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
> >
>
• 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
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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