Bernard wrote this in Hyacinthos a few years ago. ... I was wondering how one shows this. This result combines with one of my own to give this Every...
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...
I'm looking for some information which I need to my thesis. I'm going to put there something about Simson Line. And while the theorem and the proof was not so...
Dear friends, I have read in "American Mathematical Monthly", may 2006, this result: "Any inscribed triangle UVW is similar to the cevian triangle of a point...
Sorry I got circum and inconics mixed up. Here is the correct message. Bernard wrote this in Hyacinthos a few years ago. ... I was wondering how one shows...
Je reviens sur le sujet traité dans les messages 10135,10136,10146 et 10358. Après avoir pris conaissance des résultats de Darij Grinberg, je me suis...
Dear All My Friends, Given two triangles A1B1C1, A2B2C2 both inscribed in one circle (O) and one point P on the same plane. Ab = circumcenter of PA1B2 Ac =...
Dear All My Friends, In my message #14744, I remarked one concurrency when reflecting of intersections of Simson line with sidelines of reference triangle....
Dear Nikolaos Dergiades and Floor en Lyanne van Lamoen, Thank you very much. I proved the next problem: Let ABC be a triangle and the points D,E on the...
Dear Nikolaos Dergiades and Floor en Lyanne van Lamoen, Thank you very much. I proved the next problem: Let ABC be a triangle and the points D,E on the...
Dear Hyacinthos, Problem: Let ABC be a triangle and AAp, BBp, CCp three concurrent cevians at the point P. Prove that the circumcenters Ab, Ac, Bc, Ba, Ca, Cb...
My friend told me a following conjecture : Let D, E lie on the AB, AC such that EB = BC = CD Let l is a line that is perpendicular to Euler line of ABC. l is...
Dear friends, I would like if this is known: The distance from centroid G to first Fermat point is (a^2 + b^2+c^2 - 4 sqrt(3)S)/18, and the distance from G to...
http://rapidshare.com/files/17389577/HYAC4.gif.html In case this is not self-explaining: Let ABC be a triangle. Let XYZ be the cevian triangle of ABC w/res...
Dear friends Tomorrow is the Lunar New Year, the Year of the Pig, so I give all my best wishes of long life and happiness to all Asian friends of Hyacinthos, ...
Dear All My Friends, Given triangle ABC with orthocenter H. A' is reflection of A in H. Similarly define B', C'. Let X is a point with barycentrics (x : y : z)...
Dear Luis, Let A,B,C,D be the given points, where A and C are supposed to lie on opposite sides of the rhombus. Reflect the vector BD in the given line to...
Dear hyacinthos, I proved the next problem: Let's consider the triangle ABC, the point P=(p:q:r)on the circumcircle and the point Q=(u:v:w).Find the locus of ...
Dear All My Friends, Given triangle ABC and one point P with barycentrics (p : q : r) on its plane. We construct: Aa = orthogonal projection of A on sideline...
Dear colleagues! Moscow center of mathemathical education organize a geometrical olympiad in honour of I.F.Sharygin. The first (correspondence) round pass...
From the Pupils Circle: ABC is a triangle*, abc the foot points of the altitudes. Now drop the altitudes again on triangles Abc,Bac and Cab. Call their...
I have seen this problem at first exam of Korea Mathematical Olympiad Winter School. Let P be a arbitrary point in triangle ABC. Let Q be a isogonal conjugate...
Dear All My Friends, Given triangle ABC and any point X moving on sideline BC. C1 = orthogonal projection of X on AB (projection f1) B1 = orthogonal...
Dear Geometers, I found these books. The modern geometry of the triangle. By William Gallatly. http://www.amazon.com/modern-geometry-triangle-William- ...
