I want to maximize the number of similar triangles with vertices from three fixed sets, one vertex from each set. For example, if you fix two points $X$, $Y$ (i.e. two sets with only one member), then ...
Question : Is the following true? "Letting $K$ be a convex bounded closed set on a plane, then there exists a triangle $M$, which includes $K$, such that $|M|\le 2|K|$. Here, $|M|,|K|$ is the area of ...
The lines which bisect the area of a triangle form an envelope as shown in this picture It is not difficult to show that the ratio of the area of the red deltoid to the area of the triangle is ...
I've been trying to find, without much success, 4 triangles whose corresponding sides are congruent that cannot be folded into a tetrahedron. Anyone has any clue how to approach this problem?
"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 ...
Lots of simple questions because I am a noob. You are given 3 points in R^2; A, B, C forming a triangle with area > 0. You pick an arbitrary point inside ABC and an arbitrary direction. After some ...
Is there a link between the side-angle-side congruence of triangles and the parallel postulate? Specifically, does it follow from Euclid's first four axioms alone? In fact, does it even follow from ...
Be done the triangle ABC, it is known the method to finding the point Q that minimises the sum QA+QB+QC among all points Q in the plane (The Fermat point). I want a hint for solving this problem using ...