I went through the horror of creating an account to post this. If anyone ever comes across this and wants the code for Simson's theorem in Descarta2D for a college project, here it is:

<< Descarta2D`;
ClearAll;


pA = Point2D[{Cos[a], Sin[a]}];
pB = Point2D[{Cos[b], Sin[b]}];
pC = Point2D[{Cos[c], Sin[c]}];

lAC = Line2D[pA, pC];
lAB = Line2D[pA, pB];
lBC = Line2D[pB, pC];

tABC = Triangle2D[pA, pB, pC];
cABC = Circle2D[{0, 0}, 1];
pM = Point2D[{Cos[m], Sin[m]}];
IsOn2D[pM, cABC]

lMA1 = Line2D[pM, lAC, Perpendicular2D];
pA1 = Point2D[lMA1, lAC];

lMB1 = Line2D[pM, lAB, Perpendicular2D];
pB1 = Point2D[lMB1, lAB];

lMC1 = Line2D[pM, lBC, Perpendicular2D];
pC1 = Point2D[pM, lBC];

IsCollinear2D[pA1, pB1, pC1]

lSimsonA = Line2D[pA1, pB1];
lSimsonB = Line2D[pB1, pC1];

Sketch2D[{pA, pB, pC, tABC, cABC, pM, lMA1, lMB1, lMC1, pA1, pB1, pC1,
    lBC1, lSimsonA, lSimsonB} //. {a -> 0, b -> 2*Pi/3, c -> 4*Pi/3, 
   m -> 3*Pi/6}]