## 9886Re: The Brocard points of a quadrilateral (typo)

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• Jun 9, 2004
Dear Alexey,
I wrote
> suppose that ABC is a variable isosceles triangle (in B) inscribed
> in a fixed circle with center o; let M be a fixed point and A'B'C'
> the cevian triangle of M wrt ABC.

Of course, I was meaning the circumcevian triangle of M wrt ABC.
Sorry for the typo.

> It is very easy to check that the
> B'-symedian of A'B'C' intersects the line OM at a point L
> independant of the choice of ABC.
> If S is a point of the circle such as OM and OS are perpendicular,
L
> is the projection upon OM of the reflection of O wrt SM. More over
L
> lies on the half-line OM and inside the circle.
> From this it follows that if B_1,...,B_n is a regular polygon
> inscribed in the circle, if A_k is the second intersection of MB_k
> with the circle, every A_k symedian of A_(k-1),A_k,A_(k+) goes
> through L.
> That's probably a part of the proof you're waiting for.
> Friendly. Jean-Pierre
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