Find the equation of the circle that is inscribed in a triangle whose sides are 3x-4y=19, 4x+3y=17 & x+7=0.

So, by this, i got the vertices of the triangle by finding the three points of intersection. I got A(3,-1), B(-7,15) and C(-7,-10).

Please, help me figure everything out :( Thank you very much!

Question

Find the equation of the circle that is inscribed in a triangle whose sides are 3x-4y=19, 4x+3y=17 & x+7=0. 

So, by this, i got the vertices of the triangle by finding the three points of intersection. I got A(3,-1), B(-7,15) and C(-7,-10).

Please, help me figure everything out :( Thank you very much!

anonymous · Answer

The equation of the circle is:
$$(x-x_0)^2 + (y-y_0)^2 = R^2$$, where $(x_0,y_0)$ is center of the circle and $R$ is the radius.

anonymous · Answer

you have 3 points (A, B and C) and also 3 unknowns ($x_0,y_0$ and $R$). Solve for then ;)