9145Re: [EMHL] Re: excircle and circumcircle
- Jan 28, 2004Dear Darij!
>The equivalence of 2 and 5 is a particular case of next fact. Let given a
>The equivalence of the conditions 2. and 5. was the
>subject of Problem 4 in the Bundeswettbewerb
>Mathematik (German National Mathematics Olympiad)
>2002, 2 round. In fact, it was a very hard problem;
>I was lucky enough to know the method of trilinear
>coordinates to solve it!
triangle ABC and a point P. A1, B1 are the common point of AP and BC, BP and
AC. Q - a point in A1B1, Q' is isogonally conjugated to Q, A2, B2 are the
common points of AQ' and BC, BQ' and AC. Then the point P' isogonally
conjugated to P is in A2B2. This can be easily proved by trilinear
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