All Questions
8 questions
6
votes
0
answers
121
views
How many equilaterals have vertices intersections of angle trisectors of a triangle?
The celebrated Morley’s theorem ensures that the interior trisectors, proximal to sides respectively, meet at vertices of an equilateral.
In the paper Trisectors like Bisectors with Equilaterals ...
25
votes
6
answers
2k
views
Are there infinitely many "generalized triangle vertices"?
Briefly, I'd like to know whether there are infinitely many "generalized triangle centers" which - like the orthocenter - are indistinguishable from a vertex of the original triangle. This ...
- 20.5k
10
votes
2
answers
764
views
Generalization of Stewart's theorem?
I'm curious about the generalization of Stewart's theorem to more dimensions. MathWorld mentions that there is a generalization done by Bottema, but I could not find much information on it. All I ...
- 163
5
votes
1
answer
782
views
Malfatti Circles - Limiting point
"Three circles packed inside a triangle such that each is tangent to the other two and to two sides of the triangle are known as Malfatti circles" (for a brief historical account on this topic, see ...
- 667
4
votes
2
answers
320
views
Inequality from a point in plane to a triangle OR Inequality on a quadrilateral
If points $A$, $B$, $C$ form a triangle in euclidean space and $D$ is another point in the plane of the triangle, the problem is to show that :
$\frac{AB}{DA + DB} + \frac{BC}{DB + DC} \ge \frac{AC}{...
- 55
3
votes
1
answer
507
views
An new equilateral triangle related to the Morley triangle
Morley equilateral triangle is the nice theorem in Eulidean Geometry. I found an equilateral triangle and a group circle related to the Morley triangle and angle trisectors:
Let $ABC$ be a triangle ...
- 1,776
3
votes
0
answers
907
views
A generalization of the Sawayama-Thebault theorem
1. Introduction
The Sawayama-Thebault theorem is one of the best nice theorem in plane geometry. The theorem has a long history. It was published in AMM in 1938 the first solution appeared in 1973 ...
- 1,776
1
vote
0
answers
96
views
Pseudo-Droz-Farny circles
I would like to present a construction of 2 circles. These 2 circles are somewhat similar in appearance to the well known Droz-Farny circles that can be drawn for every isogonal conjugate pairs of ...
- 445