The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2008volume8/FG200814index.html The editors Forum...
ForumGeom
ForumGeom@...
May 1, 2008 4:45 pm
16338
Dear Hyacinthos, Given a circle (M,r) and two lines l and m outside the circle. The points A and B lie on the circumference of the circle. Question: To...
Dear Huub van Kempen ... [UV] is the diameter of the circle perpendicular to m. If CD is a variable chord parallel to m, the locus of the common point of AC...
If you put C on circle, and a parallel to m by C, then the locus of the intersection of AC and BD is a hyperbole passing by A, B, and the points of contact of...
Given A, b-c, r (angle A, difference of sides, inradius) draw the triangle Has anyone a simple solution? Maybe Luis already solved it ? I can solve it, but...
Dear Giovanni, Let D be the tangency point of incircle (I, r) with BC A' be the midpoint of the arc BC and M be the mid point of BC. We know that DM =...
Dear Nikos, as usual your solution opened my eyes. So following your suggestions I found another solution that seems simple and can be applied to a bunch of...
Dear Giovanni, your problem has a very simple and elementary solution, which stems from Nikos's remark about where to find b-c in the triangle. Let D and E be...
Dear Hyacinthists, Giovanni, I will print and collect the solutions already posted. My solution will be based on the following facts: i) points X and X_a are...
Hi everyone, Recently, my teacher asks me about the reference of the problem that appeared in AMM Vol. 50, No. 9, pg.561-562. A diameter d of the circumcircle...
Dear colleagues! Moscow student Pavel Bibikov formulated two interesting hypothesis which are the analogous of Euler theorems in Lobachevsky geometry. Let ABC...
Alexey.A.Zaslavsky
zasl@...
May 6, 2008 6:40 am
16348
Dear Khoa Lu and Hyacinthists, who wrote the paper you quoted? I have no acccess at Jstor. Sincerely Jean-Louis ... De : KHOA LU <treegoner@...> À :...
Dear Khoa Lu ... appeared in AMM Vol. 50, No. 9, pg.561-562. ... the side BC, CA, AB in points D, E, F. Prove that the Euler line of the three triangles AEF,...
Dear Hyacinthists, Dear Vladimir, Is it possible to use the idea of your solution to the problems and ? Best regards, Luis ________________________________ ...
Dear Luis, although the characters did not appear again, the questions are clear from the subject of your message. For A, b-c, r_a, the answer is positive: in...
Hi, To Pierre: Thanks for your suggestion. I actually don't know about this. Do you know about this problem or have a proof of it? To Jean: It is a problem...
Dear Khoa Lu [KL] To Pierre: Thanks for your suggestion. I actually don't know about this. Do you know about this problem or have a proof of it? ... Consider...
Dear Luis, Vladimir's algorithm is OK in both cases. I tested it for A, b+c, r_b , that is problem 1110 of Geometriagon (I have r_c there, but it's the same)....
Dear Hyacinthists, in response of Message Hyacinthos #8510, I propose a synthetic proof of the Mineur circle. After the nice article of Darij Grinberg, I...
Dear Tarik 1 The definition of an affine map is rather elaborate using Linear Algebra. If it is possible, look at the Berger book, Geometry, translated from...
Dear Jean-Pierre and Khoa and Tarik I must add that once we know the Euler lines are respectively parallel to the sides lines, the rest of the proof is...
Dear Hyacinthists, if you take two points B', C' respectively on the lines AB and AC, then the Euler line of AB'C' is parallel to BC if and only the Euler line...
Hello Hyacinthists, Since about two weeks I read the messages of this group. I think I have some interesting topics too. I found some conics not going through...
Dear Chris, this is the Evans conic ! http://forumgeom.fau.edu/FG2002volume2/FG200211index.html regards Bernard ... [Non-text portions of this message have...
Hi Chris, It is called the Evans conic See http://faculty.evansville.edu/ck6/encyclopedia/ETC.html at X(13) http://mathworld.wolfram.com/EvansConic.html ...
It is known that if we have two common points of two conics and other sufficient elements of each one, we can construct the other two common points; the same...
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