Dear Giovanni, you wrote ... and the trace of another median, construct the triangle." ... some time on it I don't know even if it is solvable by ruler and...
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ForumGeom
ForumGeom@...
Nov 1, 2010 4:55 pm
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2010volume10/FG201015index.html The editors Forum...
Many thanks Jean-Pierre. I'm wondering how you find that the locus is a circular cubic: by algebra or from other considerations? Best regards Giovanni Artico...
... Dear Antreas, That's pretty obvious, isn't it ? (Dilation of line AA' from center B and ratio 2 intersects circumcircle of AA'B in C) Some other related...
Dear friends, is there an easy construction of the conic bc(b-c)xx + caayy + c(aa+bb-cc)xy -baazz - b(aa+cc-bb)xz = 0 in barycentrics? Best regards Nikos...
Dear Nikos, Your conic is a circle. Let the internal and external bisector of angle A intersect BC at L and L' respectively. Then L' is the center of the...
Dear Philippe Right (and there are two solutions). I had in mind another solution: Let M be the midpoint of CB. The locus of M as C moves on the circle (AA'B)...
Dear Francisco. Very good. Thank you. The three analogous circles pass through the same point (I don't know the barycentrics) and I was expecting the isogonal ...
Dear Nikos: Your A-circle is the locus of points P such that PB^2/PC^2 = AB/AC; this easily implies that if P is on the A-circle and on the B-circle the P also...
On Wed, Nov 3, 2010 at 10:12 AM, Francisco Javier ... How about the locus of P such that PB/PC = AB^2/AC^2 (and the other two similar)? APH [Non-text portions...
Dear Nikolaos ... I think that the point that maximizes xy+yz+zx is the Mittenpunkt X[9] with maximal values rss/(r+4R) (s=semi-perimeter) If fact xy+yz+zx = k...
Dear Clark Kimberling and friends, having in mind your Hyacinthos message 18379 and your question at the end of your last FG paper "Trilinear Distance...
A mathematics teacher asks a student: -- When are two triangles congruent? Student: -- When they were made by the same confectioner! (zaxaroplastis) The...
In the general case of PB/PC = (AB/AC)^n the A-circle is centered at (0:-b^n:c^n) and has squared radius (a^2 b^n c^n)/(b^n - c^n)^2. This circle intersect the...
Dear Nikos and Francisco, 1. Francisco, your point N is also Intersectionpoint BC with A.X366. 2. There are 2 points as intersectionpoint of the 3 circles. ...
Dear friends, according to ETC, the points with trilinears cos(A/3 + t) : : and sin(A/3 + t) : : should lie on the line X(16), X(358). I suspect that X(16) is...
I repeat with a correction to a sign Dear Bernard, the point X(16) (sin(A -pi/3) : sin(B -pi/3) : sin(C -pi/3)) and the points (sin(A/3 + M) : sin(B/3 + M) :...
Dear Bernard, I forgot to say that the factorization (x-y)(y-z)(z-x)(1+xy)(1+yz)(1+zx)Q.R contains the factor (1+mn) and that the determinant of points (sin(A...
Dear Francisco and Nikolaos, thank you for your answers that infirm what I had suspected. however, I'm still unhappy about this for two reasons : 1. the proofs...
... Natural question. Perhaps X(15) is involved in another collinearity with points cos(A/6 + t) ::, sin(A/6 + t) ::, or something similar. aph [Non-text...
Dear Bernard, here is a proof without computer. If a = A/3, b = B/3, c = C/3, p = pi/3 = a + b + c then the trilinears of the 3 points X(16), P, Q are sin(3a -...
Dear Triangle Geometers, Fermat point is the for real numbers t,u,v, identifying the point such that tAP+uBP+vCP takes extreme value can be considered as the...
Dear Sung Hyun,  I send you some results concerning Fermat points (unfortunately are in Romanian, but you can use google translator). Best regards, Catalin...
Dear Hyacinthists, \pm means + - Do the problems A,a,r_b\pm r have a R&C construction? As always, thank you for your valuable time/information. Luis [Non-text...
