- Let ABC be a triangle, L a line and La, Lb, Lc its reflections in

BC,CA,AB, resp. Denote A'B'C' the triangle bounded by

the lines L1,L2,L3.

There was a discussion here about properties

of the triangle A'B'C'. See message

16734<http://tech.groups.yahoo.com/group/Hyacinthos/message/16734>

Here is another one:

Let HaHbHc be the orthic triangle.

The circles (A'AHa), (B'BHb), (C'CHc)

are coaxial.

aph

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http://anopolis72000.blogspot.com/2012/01/2o.html - Which is the locus of the 2nd intersection of the circumcircles of NA'A", NB'B", NC'C", as L moves around O?The locus of the 2nd intersection of the circumcircles of HA'A", HB'B", HC'C", as L moves around O, is the circumcircle of ABC.The circumcircles of PA'A", PB'B", PC'C" are coaxial.Let ABC be a triangle, L a line and P, Q two points.The L intersects BC, CA, AB at A', B', C', resp. and AQ, BQ, CQ at A",B", C", resp.Special Cases:Let L be passing through O, intersecting BC, CA, AB at A', B', C', resp. and AH, BH, CH at A", B", C", resp.

In general, if P is a fixed point, the locus of the 2nd intersection of the circumcircles of PA'A", PB'B", PC'C", as L moves around O, is a conic?APH