Dear friends

I notice the following fact certainly well known for a long time and very

easy to prove:

Call P any point in the plane of triangle ABC and L the trilinear polar of P

wrt ABC.

Call Gamma the inscribed conic in ABC of which P is the perspector or

Brianchon point, i.e : P is the perspector of ABC and the contact triangle.

Let M be any point on Gamma and call T the tangent in M at Gamma.

Then the trilinear pole O of T is on L.

From this fact can we find :

1°a simple projective construction of the tangent T of M at Gamma.

2°If O is any point on L, a simple projective construction of the contact

point M of the trilinear polar T of O wrt ABC with Gamma.

Thanks for your swift replies

François

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