Dear Floor van Lamoen, and Hyacinthos, Since we have started to investigate Miquel points, here are two "forgotten" theorems on them. The Miquel point...
Dear Darij ... CA'B' ... M' ... It is well known (Steiner 1827) that Ma,Mb,Mc,M,P are concyclic (Miquel cirle of the quadrilateral). Hence, this theorem is not...
Dear friends of Hyacinthos happy 2003 a problem of Cubles Cabri http://www.oma.org.ar/enunciados/9na3era.htm Given three points D, E and F, to construct an ABC...
RICARDO BARROSO CAMPOS
rbarroso@...
Jan 1, 2003 11:46 am
6242
Dear Darij ... are ... of ... BC'A', ... I ... Using oriented angles of lines (modulo Pi) <PXaX = <PXaA = <PC'A = <PC'B = <PXbB = <PXbX and Xa,Xb,P,X are ...
Dear Ricardo and other Hyacinthists ... that points D, E and F are the intersections between bisector of A and the perpendicular bisector of BC; bisector of B...
Let D be a point on the circumcircle of a triangle ABC. Then, as we know, the projections X, Y, Z of the point D on BC, CA, AB lie on one line p (called the...
Dear Floor van Lamoen and folks interested in the Droz-Farny theorem, Some days ago, I have found a proof of the Droz-Farny theorem after a wonderful idea of...
1) ABCD is a quadrilateral with diagonal [AC]... There is a point E on [AC] such that m(ADE)=m(CDE) and m(ABE)=2.m(CBE)... if m(DAC)=30 , m(ACD)=42 and...
Dear Darij, ... Then, as we ... lie on one ... theorem is that ... equality ... In F.G.-M. 1212a (theorem 358-I) this DA * DX = DB * DY = DC * DF = 2Rd, is...
Dear John Conway, Steve Sigur, and the rest of the group, You might know the following theorem: 1. If Na, Nb, Nc are the centers of the Neuberg circles of...
Dear Nikolaos Dergiades, Thanks for the reference. I think the relation can be used for some studies on harmonic quadrilaterals. By the way, I mistyped DA * DX...
... i found the second problem's solution after i sent it... sorry for wasting your time... PROBLEM: D is a point in a triangle ABC such that m(ABD)=75,...
A happy new year to everyone. I'd like to follow up on Floor's note and Darij Grinberg and Aad Goddijn's proofs. ... Yes, indeed. ... First, the results are...
Dear Alex ... 77-82, ... there ... If we use the Poncelet theorem : The center of a rectangular hyperbola circumscribed to a triangle lies on the NP-center of...
(Answer to Hyacinthos message #6240) ... If I understand correctly, you assume that A', B', C' are collinear. But they need not be! Therefore, the Baum theorem...
Dear Darij, ... collinear. ... Yes, you are perfectly right; I thought that you were talking about the Miquel point of a complete quadrilateral. With my...
... Somehow this must be connected with the famous Fontene theorems, but I have no time to look further at it. I am sure that it can be proven elementarily...
Dear Jean-Pierre: ... Simple, but not elementary. For the definiteness' sake, I think that anything beyond "Geometry Revisited" is not elementary. All the...
Dear Alex and friends on Hyacinthos, Happy New Year. [AB]:... ... Dear Alex, The line in question is the one joining the center of the circle to the centroid...
Dear Paul: Thank you. It could not be clearer. ... If f(t) = t/(1+t), then f(0) = 0, f(1) = 1/2, f(1/2) = 1/3, and f(1/3) = 1/4. So indeed f(1) - f(1/3) =...
Dear Darij: ... Yes, Coolidge mentions Fontene several times in the neighborhood of that theorem. For example in a footnote:) "Fontene speaks of this as a...
Dear Darij, I've tried to find an easy synthetic proof of Braun theorem ... are ... CA'B' ... M' ... PaPbPc is the pedal triangle of P. A direct similitude...
Dear Hyacinthists, can you "synthetically" prove this problem: PROBLEM: Let P, Q two points respectively on the sides BC and CD of the square ABCD such that...
Dear Alex, Paul, You are right, of course, about this Euler line of a cyclic quadrilateral. In my note in Hyacinthos #932 I gave the center (Q in my note,...
Dear Ercole Suppa, We first observe that angle PAQ is 45 degrees (Let PQ touch the circle at T. AP bisects angle TAB and AQ bisects angle TAD .Angle BAD is a...
Dear Droz-Farny friends (*), "Given triangle ABC with orthocenter H. A rectangular hyperbola with center H intersects line BC in A1 and A2, line CA in B1 and...
Dear Paul, Alex, There was a mistake in my last reply, as you probably noticed. I combined the right homotheties, but to quick and not in the right way... ...
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