# Questions tagged [analytic-geometry]

Questions on the use of algebraic techniques for proving geometric facts. Analytic Geometry is a branch of algebra that is used to model geometric objects - points, (straight) lines, and circles being the most basic of these. It is concerned with defining and representing geometrical shapes in a numerical way.

6,732 questions
Filter by
Sorted by
Tagged with
100 views

### Convergence of the sequence of the orthocenters, incenters and centroids of a triangle.

Now asked on MO here. Given a scalene triangle $A_1B_1C_1$ , construct a triangle $A_{n+1}B_{n+1}C_{n+1}$ from the triangle $A_nB_nC_n$ where $A_{n+1}$ is the orthocenter of $A_nB_nC_n$, $B_{n+1}$ is ...
23 views

### Determining the Plane for a Given Point and Line Using the Equation of a Plane

I was working on an exercise following an example that required exactly what I had to do as well, but I encountered some difficulties. Below, I have indicated 2 titles, the first one is the example I ...
159 views

88 views

### Is there a faster way to find max and min of $P = 4x + 2y + 3$ given $|x| + 2|y| = 4$?

Is there a faster way to find max and min of $P = 4x + 2y + 3$ given $|x| + 2|y| = 4$? From a geometrical standpoint, the set of points that satisfy $|x| + 2|y| = 4$ is a diamond on the $Oxy$ plane. ...
1 vote
15 views

1k views

### Deriving the barycentric coordinates of a triangle's orthocenter, using the areal definition of such coordinates

Wikipedia's "Altitude (triangle)" entry describes the barycentric coordinates of $\triangle ABC$'s orthocenter as $$(\tan A : \tan B : \tan C)$$ How would you prove this using solely the areal ...
50k views

### How can you construct as many intersections as possible with n lines?

If you have $n$ lines, it seems to be obvious that you can have at most $\frac{n^2-n}{2}$ intersections: $n = 1$: Obviously you need two lines to intersect, so the maximum number of intersections is ...
45 views

### General proof of this special triangle property

Consider any general triangle $ABC$ contained in a two dimensional plane. Three circles are drawn having the sides of triangle $ABC$ as diameters. Prove that the centre of the circle, which is ...
21 views

### Determine MPH of a Sphere From Diameter Change Using Image Processing

I'm looking for a formula to calculate the speed of a ball coming directly at or away from you solely based on the the change in diameter over time. For example, if I video recorded a ball that was a ...
### An ellipse $\mathcal{E}$ touches a fixed ellipse $\mathcal{C}$ at $A$, prove the length of semi-major axis of $\mathcal{E}$ is constant
$\mathcal{C}$ is an ellipse with center $O$ and semi-major axis length $=a$, semi-minor axis length $|OB|=b$. $A$ is a point moving on $\mathcal{C}$. $E$ is a point on $\mathcal{C}$ such that $OE$ is ...