Dear friends, Relax the definition of point and consider the vertices of our triangle as being elements (skewed circulants for example.) Can we then define the...
Dear Hyacinthists, If <P1,P2> and <P3,P4> are harmonic conjugates, then the circles having P1P2 and P3P4 as diameters are orthogonal. Is the converse true? ...
Dear Luis, ... Yes. Let the circle with diameter P1P2 and center O is orthogonal to the circle with diameter P3P4 and center O' and the points P1, P2, P3, P4...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2007volume7/FG200713index.html The editors Forum...
ForumGeom
ForumGeom@...
Jun 5, 2007 7:03 pm
15308
Dear All My Friends, I continue study on theme "One Is Sum Of Other Two" and have found one simple fact: Antiorthic axis is the locus of point such that three...
Dear Tuan Observe that the TRILINEAR coordinates of a point are proportional to the SIGNED distances from the sidelines. Thus, the locus of points for which...
Dear Hyacintheans. I have a problem that I don't know how to solve it. So I will need help from many experts. Thank you so much in advance. Given triangle ABC...
Dear Quang Tuan Bui ... from this point to three sidelines of reference triangle hold a property "one is sum of other two". I think that your locus is the...
Dear Jean-Pierre and Wilson, Thank you very much for your advices. You are both right. May be because the fact is very very simple so no where it is mentioned....
Dear Jacob, ... Your point J is X(174) and I think is in the same area with the point X(177) as defined in my proof in Hyacinthos message 14540. Hence <JIG >=...
Dear Jacob, Sorry again, It is not correct that <JIG >= 120 because the three inequalities <JIG >= <BIC = 90 + A/2 <JIG >= <CIA = 90 + B/2 <JIG >= <AIB =...
Dear Nikos Dergiades Thank you very much for your interest and your reference, I will think about them carefully. Actually I want to prove that inequality...
Dear Francois, I thought maybe by "complexification" you meant a 'complicated number' like that defined in [1] below. ... Sincerely, Jeff [1] I.J. Good, "A...
Hello all, How would you prove that an injective mapping from the euclidean plane into itself which sends circles to circles and lines to lines also preserves...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2007volume7/FG200714index.html The editors Forum...
ForumGeom
ForumGeom@...
Jun 12, 2007 6:59 pm
15321
Dear Julien ... plane ... a ... supplementary) ... surjective) ... It is classical that, as f maps a line to a line, f is affine. So, as f maps a circle C with...
Let ABC be a triangle and O its circumcenter. The lines AB and AC meet the circumcircle of triangle BOC at two points B' and C' (apart from B and C ),...
... meet ... from B and ... BC and B'C'. ... center on the ... Here is an idea, but without inversion Check that OB' and AC are perpendicular; so do OC' and...
Dear Hyacintheans, I have found a following result Given triangle ABC and A'B'C' is orthic triangle Ia,Ib,Ic are incenters of triangles AB'C',BC'A',CA'B' then...
Dear Hyacintheans, I have found a following result Given triangle ABC and A'B'C' is orthic triangle Ia,Ib,Ic are incenters of triangles AB'C',BC'A',CA'B' then...
Emelyanov
tl_em@...
Jun 16, 2007 9:09 pm
15326
The following paper has been published in Forum Geometricourm. It can be viewed at http://forumgeom.fau.edu/FG2007volume7/FG200715index.html The editors Forum...
ForumGeom
ForumGeom@...
Jun 18, 2007 4:27 pm
15327
This problem II.198 in "Planimetric problems" from I. F. Sharygin: Let D, E, F the feet of internal angle bisectors of triangle ABC. Show that one of the...
Dear Francisco If A', B', C' are the intersections of the circumcircle of DEF with the sides of ABC let x = BA'- BD y = CB' - CE z = AC' - AF x, y, z are the...
Dear All My Friends, Given triangle ABC with one point P with barycentrics (p : q : r) and any point X with barycentrics (x : y : z). Three lines La, Lb, Lc...
Dear Francisco ... Show ... of ... This problem is also true for the circumcircle of the cevian tiangle A'B'C' of one of the excenters of ABC (not only for the...
Dear Quang Tuan Bui, ... Don't you think it's better to say that the three signed distances sum up to zero, the triangle ABC being arbitrarily orientated. ... ...
