I’ve got a rather complicated geometry problem that I’m trying to solve – how to find the intersection between two triangles in 3D space. I’ve looked around at other questions and answers on this site and quite a few others, but none of them seem to satisfy my question. Anyway, given two triangles on two […]

Is it possible to find the angles of a triangle if I only have its sides? If so, how can I achieve this? Regarding my knowledge of triangles: Whilst I was taught trigonometry a few years ago, I cannot for the life of me remember how to do things like use SOHCAHTOA to figure out […]

I have the following problem: In my class, we did a majorly complicated method to figure this out but I think there is a better way to do this… Here is the exact problem: A belt fits snugly around the two circular pulleys shown. Find the distance between the centers of the pulleys. Round to […]

Just for fun read few problems on the projeteuler.net website. Number 276 found interesting: Consider the triangles with integer sides a, b and c with a ≤ b ≤ c. An integer sided triangle (a,b,c) is called primitive if gcd(a,b,c)=1. How many primitive integer sided triangles exist with a perimeter not exceeding 10 000 000? […]

I had searched online and found an equation that solves the radius of a circle from 3 points that are located on the circumference of that specific circle. Where I had found this formula did not state its derivation or anything of the likes, however it is to find the radius. With the 3 points, […]

Prove that $$\frac a{b+c}+\frac b{c+a}+\frac c{a+b}\lt 2$$ given that $a,b,c$ are sides of a triangle. I know that the above is $\ge \frac32$ but how will you prove the above? I know this might sound a bit basic but please help.

Prove that $AH^2+BC^2=4AO^2$, where $O$ is the circumcentre and $H$ is the orthocentre of the triangle $ABC$.

See this figure ABC is a triangle. R is a point inside that triangle, specified by its barycentric coordinates. w is a scalar. We mark the points B’ and C’ such that BB’ == w and AB’ == AB – w CC’ == w and AC’ == AC – w My question is, given the […]

The question is as simple as that, but I have been trying to figure out an answer (and searching for it) with 0 results. I mean, given two triangles (in 2D) I want to find just a single point which they may have in common. Of course I have the long solution consisting of looking […]

$$a \cdot \sin (B-C) +b \cdot \sin(C-A) +c \cdot \sin(A-B) =0$$ where $a, b, c$ are the sides of a triangle and $A, B, C$ are the angles of a triangle. No idea how to solve this problem.

Intereting Posts

How many trees in a forest?
Interpolation inequality
Explanation of the Fibonacci sequence appearing in the result of 1 divided by 89?
Proving the Product Rule for exponents with the same base
Can all circles of radius $1/n$ be packed in a unit disk, excluding the circle of radius $1/1$?
Calculate logarithms by hand
Prove that if $(v_1,\ldots,v_n)$ spans $V$, then so does the list $(v_1-v_2,v_2-v_3,\ldots,v_{n-1}-v_n,v_n).$
For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})…(1- \frac{1}{n^2}) = \frac{n+1}{2n}$
Bhattacharya Distance (or A Measure of Similarity) — On Matrices with Different Dimensions
How to factor $a^n – b^n$?
Combinatorics identity question
Integral $\int_1^2 \frac1x dx$ with a Riemann sum.
Product-rule for Jacobian calculation, i.e. $\frac{d}{dx}(Ay)$ where A is a matrix and y a vector and both depend on x
Can a collection of points be recovered from its multiset of distances?
How to find $\lim _{ n\to \infty } \frac { ({ n!) }^{ 1\over n } }{ n } $?