Assume ABC is a triangle and a circle K with center P and radius r intersects the sides (NOT the straight lines which make ABC!) in 6 points (which means r...
See file. By default the blue quadrangle UVWX has one green "complete triangle" ABC (at least that's how they are called in German?!), and counting free...
I recap: Draw three diameters UX,VY,WZ of a conic K with midpoint M such that their endpoints lie on the sides AB,BC,CA of a triangle. (See uploaded file.) ...
In message #1006 by Edward Brisse I read: "Construct the common pole P to incenter and circumscribed circle to ABC" I don't know what this is and how to...
Hi all, I'm bringing up a good old topic. It may well have been known, even well-known... [let W=capital Omega, and by Steiner ellipse I mean Steiner...
Of course I'm only joking - what I mean is that I work purely algebraically and thus can use wacky things like circle with negative or even imaginary radii...
Let P be a center foo of ABC. (P should better be always inside of ABC, but the process *might* also converge if not.) Let A'B'C' be the cevian triangle of...
Dear hyacintos the trilinear line of the ideal point P = [m:n:p] with m+n+p = 0 has barycentric equation u/m+v/n+w/p = 0 When p descrive the ideal line, this...
Dear friends, Next circles through X5 have the same radius: * circle through X5, X3, X114, X182 * circle through X5, X3, X127, X141 * circle through X5, X125,...
Are you sure of that? If I understand you, X would be the centroid of the quadrilateral, Y the centroid of the sides and Z the centroid of the vertices? ...
Dear Hyacinthians, I am struggling with the following problem: Version A --- Let be given a quadrilateral ABCD (which may be non-convex or self-intersecting)...
Dear Hyacinthists, e_b := B external bisector One can construct (Euclides) 2 triangles given (A,e_b,r_a). But how about (A,e_b,r_c)? I wasn't able to construct...
Someone always had had the idea before, but anyway :-) Consider a center foo of triangle ABC to have trilinears x:y:z. Then I define the outer foo centers to...
Dear friends! Happy New Year! Here is a link for geometrical olimpiad in memory of I.F.Sharygin. http://www.geometry.ru/olimp.htm Best regards, Alexei...
Which of these conditions guarantee that a triangle is isosceles? a) Two altitudes have same length. b) Two side bisectors have same length. c) Two angle...
1. Draw circles with radii b,c,a around A,B,C. Call the radical center of these circles R1. 2. Draw circles with radii c,a,b around A,B,C. Call the radical...
Dunno if Darij already reported this (when we produced radical centers by the score, the ETC was *much* shorter). Anyway. Draw three circles around A,B,C with...
To recap: Build a tetrahedron ABCD and project D into the plane ABC to get P. Demand f(AB,CD)=f(AC,BD)=f(BC,AD). Let f be... P traces... quotient -> Euler...
One free book I like (from http://pdg.lbl.gov/ ) is the Particle Data Booklet. Anyone can get it free, and it is updated roughly yearly. One new section is...
I think I have posted some of this already way back, but it's not trivial to browse the archive. :-) Basic construction: Let ABC be a triangle and D a point in...
Must...not...post. Must...not...post. Too late, and it's Silvester night anyway. Some smart alec observed that the "34" of Rule 34 is a Fibonacci number. The...
Dear friends, 1. Name intersection points line perpendicular at X3 to the Eulerline with circumscribed circle P1 and P2. 2. Construct lines L1 and L2 through...
Dear Bernard and dear friends It is known that the shapes of repeated triangles wrt a fixed point P recur with period 3 and the Mac Cay cubic is the locus for...
What is the locus of the all the foci of the circumparabolae of a given triangle ABC? (b: Same as a, only rectangular hyperbolae instead of parabolae) Hauke ...
Dear Hyacinthists, The following problem is from a math group. ... ABCD is a given inscriptible quadrilateral. Vertices A and B belong to a branch of an ...
So, a conic has 1 center, 1-2 foci and the one or other interesting point at infinity...but do higher curves (like the Neuberg cubic or whatever) have analog...
Dear Hyacinthists, Now that it is almost Christmas it is a good opportunity for me to introduce a special configuration (with a nice star) I have been ...
I drew the conic K through A,B,C,#15,#16 (has to do with my quartet searching). Its intersection with the Neuberg cubic other than A,B,C,#15,#16 is #1138....
For a given point P, let Ha be the hyperbola with foci at B and C and passing through P. Cyclically define hyperbolas Hb and Hc. Ha, Hb, and Hc will concur...
