... Dear extreme trianglist, There is still a little bit not quite correct in Your solution in case (2) i.e. P and A,B are on different sides of ell. We have...
sin(2A + B) If ------------ := k, sinB tan(A+B) compute --------- in terms of k. tanA PS: I modified the problem found in: F. Michel - M. Potron : La...
... Here is it: Let ABC be the reference triangle. Consider the rectangular circumhyperbola (Hp) centered at P = (u:v:w) [a point on the NPC of ABC]. 1....
... Let's copy another problem from the above book (pp. 1-7; annee 1901): Soient Ox, Oy deux axes de coordonnees rectangulaires, soient a et a' les abscisses...
Let ABC be a triangle. Find the locus of P in 3D such that: PA^2 - a^2 = PB^2 - b^2 = PC^2 = c^2. Antreas PS: This problem (but in different wording) was given...
Dear friends, What is the locus of P for which the centers of the squares inscribed in triangles PBC on the side BC, PCA on CA, and PAB on AB form a triangle...
... The locus of P such that AA", BB", CC" are concurrent is the circumcubic with equation (in 3linears): x(y-z)[(y+z)cosBcosC - xcosA] + y(z-x)[(z+x)cosCcosA...
let ABC be a triangle and A'B'C' the pedal triangle of a point P. Denote PA' = x, PB' = y, PC' = z (actual 3linears of P). Let A", A* be two points on PA' (see...
Dianzhou Zhang, Professor of Mathematics, East China Normal University, Shanghai, is co-chair of a committee whose charge is to redesign high school...
Dear friends, A and B are two points on the same side of a line ell. To locate (construct if possible) a point P such that the sum of the distances from P to...
Neuberg Theorem (1897): Let l be a line intersecting the sides BC,CA,AB of the reference triangle ABC at A1,B1,C1, respectively, and D a point on the...
[APH] ... In the general case: ABC = arbitrary triangle, the AA', BB', CC' concur iff M lies on our old friend (Neuberg cubic). On the other hand, if A',B',C'...
Soient A',B',C' les symetriques d'un point M par rapport aux cotes BC,CA,AB d'un triangle equilateral ABC. Demontrer que les droites AA',BB',CC' sont...
Soient un triangle ABC et deux points D et E qui parlagent harmoniquement le cote BC. Demontrer que le cercle ADE passe par un point fixe [...] (JdME...
Anallagmatic cubics, part 9. ABC are the vertices of the reference triangle. w1, w2 are conjugate points (these notes default to isotomic conjugate with ...
... The locus is a quartic: We have the trigonometrical identity: q + u + v + w = 180 d. ==> tanq + tanu + tanv + tanw = tanutanvtanw + tanvtanwtanq +...
I included Hyacinthians because of the Greek connexion. While still a teen-ager I learned from Dickson the word `pronic'. E.g. in his footnote reference to ...
Let ABCD be a quadrilateral and P a point on its plane. Which is the locus of P such that: ang(PAB) + ang(PBC) + ang(PCD) + ang(PDA) = 180 deg. ? APH...
Hi, all. My conjecture is the following : Let P be in the interior of triangle ABC, and let the lines AP, BP, CP intersect the sides BC, CA, AB in L, M, N,...
Anallagmatic cubics, part 8. ABC are the vertices of the reference triangle. w1, w2 are conjugate points (these notes default to isotomic conjugate with ...
Dear all, Keith Dean and I have been discussing some constructions for reciprocal conjugacies (terminology?) lately. That is conjugacies mapping x:y:z --> u/x...
