Dear Hyacinthists with my best greetings for 2011 for you, your family and your friends, I have a little question : Consider a quadrilateral A_1,A_2,A_3,A_4 ...
Let ABC be a triangle, P a point, Ab the other than A intersection of AB with the circumcircle of AHC and Ac the other than A intersection of AC with the...
Dear Hyacinthists, an article concerning the Kantor-Hervey’s point has been put on my website http://perso.orange.fr/jl.ayme    vol. 6 Le point de...
Let ABC be a triangle, O its circumcenter, and L a line. Let A', B', C' be the orthogonal projections of A,B,C on L, resp. Which is the envelope of L such that...
Dear Hyacinthists, Let ABC be a triangle. M a point on the line BC. P_a the parabla of focus A and directrix BC. P_1 and P_2 the parablas of focus the...
Dear Antreas, [APH](19845): Given triangle ABC and its circumcircle (O). Construct the circle (Oa) which is tangent to [the segment] BC and tangent to (O) at...
Dear all, Does anyone know formula for obtaining intersections of polar of point X wrt conic with matrix M? (Intersections can be non-real of course) Regards, ...
Dear friends, I want to teach my students some triangle geometry in the upcoming semester. I am going to dedicate one og the elective units in the program to...
Good Day Everyone, I just would like to ask if you know some of the properties of Morley's Triangle? I really have limited resources. =) Thanks, and have a...
Dear triangle geometers, Sorry about the recent bombarding of random questions. This question is a short one though, and it should be easy. What is the locus...
Dear all, Does anyone know a formula that converts point (x,y) in Kiepert Cartesian Coordinate (Cartesian coordinate based on two axes of Kiepert Hyperbola) ...
Hi all, I have this problem Let ABC be a triangle and M(x,y,z). Let A_1B_1C_1 be the cevian triangle of M wrt ABC. Let A_2, B_2, C_2 be respectively the second...
Dear Hyacinthists, Consider the problems: 1) A,h_a,r+r_b 2) A,h_a,r_b-r 3) A,h_a,r_a+r_b 4) A,h_a,r_a-r_b 5) A,h_a,r_b-r_a Do they have a R&C construction? ...
Dear all, I'd like to ask a question that is probably trivial using some short projective geometry (that I am yet to learn...) Do two arbitrary conics always...
Dear Hyacinthists, an article concerning the ‘’Euler-Poncelet’’ point has been put on my website http://perso.orange.fr/jl.ayme    vol. 8 Le point...
Consider the following question: Find all functions f(x,y,z)=homogeneous coordinate of function in x,y,z such that if we take D=f(a,b,c), A=f(BC,CD,DB) of BCD,...
Dear Hyacintists, let ABC be a triangle, XYZ the ortic triangle of ABC, Â (O) the circumcircle of ABC, 1a, 1b, 1c the resp. A, B, C-excircles of ABC, PQR the...
To construct triangle ABC if are given A, h_b + a, h_c + a (where h_b,h_c are the altitudes from B,C) APH [Non-text portions of this message have been removed]...
Dear all, Locus of center of conics that pass through m points and n lines is respectively: (m,n)=(4,0) -> Conic (Nine-Point Conic) (m,n)=(3,1) -> ?? ...
To construct triangle ABC if are given A, 2b + a = m, 2c + a = n APH http://anthrakitis.blogspot.com/2011/01/triangle-construction-2ba-2ca.html [Non-text...
Dear Hyacinthists, Let a,b,c are sides of triangle ABC, s - semiperimeter, R - circumradius and r incircle radius. 1) Find the sum a^2 + b^2 - c^2 in function...
Dear Hyacinthists, Both A, a+b+c, R+r and A, b+c-a, R+r have a TC. How about A, a + b - c, R+r ? Best regards, Luis [Non-text portions of this message have...
We have seen before this triad of circles: Let ABC be a triangle and (Ka) the circle touching the circumcircle at A and the sideline BC. Similarly (Kb), (Kc). ...
of THIS <http://anthrakitis.blogspot.com/2011/01/inradius-3.html> ? http://anthrakitis.blogspot.com/2011/01/inradius-3.html Let ABC be a triangle D, a point...
Dear Hyacinthists, Antreas, Considering your message on this subject, I recalled the one below. It could be the fourth solution you are looking for. I saw the...
Dear friends, Let f x^2 + g y^2 + h z^2 + 2 p y z + 2 q z x + 2 r x y = 0 be the equation of a conic. As Nikos told earlier we can see from the matrix ... the...
Let ABC be a triangle and A'B'C' the pedal triangle of a point P. The line PA' intersects the circumcircle of PBC at (P and) A". Similarly we define the points...
