Articles of triangle

How do I find the Intersection of two 3D triangles?

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 […]

How do I find the angles of a triangle if I only have the lengths of the sides?

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 […]

Finding the distance between two gears

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 […]

Does “triangle” in English exclude degenerate triangles?

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? […]

How does this equation to find the radius from 3 points actually work?

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, […]

Proving an extension to nesbitts inequality: $\frac a{b+c}+\frac b{c+a}+\frac c{a+b}\lt 2$

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 $AH^2+BC^2=4AO^2$

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

Determine if a point is inside a subtriangle by its barycentric coordinates

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 […]

Point inside the area of two overlapped triangles

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 […]

Trigonometric relation between sides and angles of a triangle

$$a \cdot \sin (B-C) +b \cdot \sin(C-A) +c \cdot \sin(A-B) =0$$ 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.