I have the following equations: , , .These equations determine a triangle.I have to find the incenter coordinates.
I found the coordinates of the triangle vertices and all I know is that I take the incenter point then
How to continue?
geometry
I have the following equations: , , .These equations determine a triangle.I have to find the incenter coordinates.
I found the coordinates of the triangle vertices and all I know is that I take the incenter point then
How to continue?
Best Answer
Guide:
It is know that for a $\triangle ABC$, suppose its length is $a,b,c$, with the vertices being $(x_i, y_i)$ where $i\in \{A,B,C\}$.
Then the formula is given by
$$\left( \frac{ax_A+bx_B+cx_C}{a+b+c},\frac{ay_A+by_B+cy_C}{a+b+c}\right)$$
A proof of the formula can be found here.
You have found the coordinates, hence it should be possible for you to find the lenght of the sides easily.