I am trying to to inscribe a circle in a given triangle but it isn't working. I've used GeoGebra with this construction and worked but as I'm new to Mathematica, I am missing something. It can't be so complex to do. Here is my code:
pA = {0, 0}; pB = {1.1, 1}; pC = {1.5, 0}; midAB = (pA + pB)/2; midBC = (pB + pC)/2; midAC = (pA + pC)/2; myT = Triangle[{pA, pB, pC}]; centerC = (midAB + midBC + midAC)/3 raioC = Last[centerC] Graphics[{EdgeForm[Directive[Thick, Blue]], White, myT, {PointSize[Large], Red, Point[midBC]}, {PointSize[Large], Red, Point[pA]}, {Orange, Line[{pA, midBC}]}, {Orange, Line[{pB, midAC}]}, {Orange, Line[{pC, midAB}]}, {Red, Circle[centerC, Last[centerC]]}, }, AspectRatio -> Automatic, PlotRange -> All]
I understand that I'm not doing right the radius of the circle but I've tried more than one way to do that.
Here is the original (book) construction:
To construct: The circle inscribed in $\triangle ABC$
Construction: Construct the bisectors of two of the angles of $\triangle ABC$. Their intersection is the center of the required circle, and the distance (perpendicular) to any side is the radius. (Any point on the bisector of an angle is equidistant from the sides of the angle.)
As I said, it worked in GeoGebra and it is almost working with my code. Thank you for any help.