# NinePointCircle: Nine Point Circle In geophys: Geophysics, Continuum Mechanics, Mogi Models, Gravity

## Description

Nine Point cirlce of a triangle

## Usage

 `1` ```NinePointCircle(P1, P2 = c(0, 1), P3 = c(1, 0), add = FALSE, SHOW = TRUE) ```

## Arguments

 `P1` vector, Point 1 `P2` vector, Point 1 `P3` vector, Point 1 `add` add to existing plot `SHOW` create a new plot and add

## Details

circle passes through nine points that can be calculated for any triangle. Also known as Feuerbach's circle, Euler's circle, Terquem's circle, the six-point circle, the twelve-point circle, the n-point circle, the medioscribed circle, the mid circle, the circum-midcircle.

## Value

list of essential points:

 `A` 2-vector, vertex point 1 `B` 2-vector, vertex point 2 `C` 2-vector, vertex point 3 `D` 2-vector, mid-point opposite A `E` 2-vector, mid-point opposite B `F` 2-vector, mid-point opposite C `G` 2-vector, foot altitude point opposite A `H` 2-vector, foot altitude point opposite B `I` 2-vector, foot altitude point opposite C `J` 2-vector, mid point from S-A `K` 2-vector, mid point from S-B `L` 2-vector, mid point from S-C `S` 2-vector, Intersection point of altitudes `CEN` 2-vector, center of nine point circle `R` radius of nine point circle

## Author(s)

Jonathan M. Lees<[email protected]>

## References

http://en.wikipedia.org/wiki/Nine-point_circle

 ```1 2 3 4 5``` ``` P1 = 10*runif(2) P2 = 10*runif(2) P3 = 10*runif(2) TRI = NinePointCircle(P1, P2, P3, add=TRUE, SHOW=TRUE) ```