Gergonne Point, can't find coordinates of points of tangency of the inscribed circle
This is my attempt to demonstrate properties of Gergonne point, but i'm new in mathematica and have troubles with finding points of tangency for inscribed circle...
InCircle[{x1_, y1_}, {x2_, y2_}, {x3_, y3_}] := With[{
u = Norm[{x2, y2} - {x3, y3}],
v = Norm[{x3, y3} - {x1, y1}],
w = Norm[{x1, y1} - {x2, y2}]},
Circle[(u {x1, y1} + v {x2, y2} + w {x3, y3})/(u + v + w),
1/2 Sqrt[-(((u - v - w) (u + v - w) (u - v + w)))/(u + v + w)]]];
Manipulate[
Graphics[{Thick, Green, Line[{a[[1]], a[[2]], a[[3]], a[[1]]}], Red,
Thick, InCircle[a[[1]], a[[2]], a[[3]]], Red,
PointSize[Large],Point[{a[[4]]}]},
PlotRange -> 6.0], {{a, {{-1, -1}, {1, -1}, {0, 1}}}, Locator}]
InCircle[{x1_, y1_}, {x2_, y2_}, {x3_, y3_}] := With[{
u = Norm[{x2, y2} - {x3, y3}],
v = Norm[{x3, y3} - {x1, y1}],
w = Norm[{x1, y1} - {x2, y2}]},
Circle[(u {x1, y1} + v {x2, y2} + w {x3, y3})/(u + v + w),
1/2 Sqrt[-(((u - v - w) (u + v - w) (u - v + w)))/(u + v + w)]]];
Manipulate[
Graphics[{Thick, Green, Line[{a[[1]], a[[2]], a[[3]], a[[1]]}], Red,
Thick, InCircle[a[[1]], a[[2]], a[[3]]], Red,
PointSize[Large],Point[{a[[4]]}]},
PlotRange -> 6.0], {{a, {{-1, -1}, {1, -1}, {0, 1}}}, Locator}]
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