size(12cm);
usepackage("hwemoji");
pair P = dir(80);
pair A = dir(210);
pair B = dir(330);

draw(A--B, red);

pair D = foot(P, A, B);
pair H_1 = orthocenter(P, A, B);
pair H_2 = midpoint(P--H_1);

pair E_1 = extension(A, H_1, P, B);
pair E_2 = extension(A, H_2, P, B);
pair F_1 = extension(B, H_1, P, A);
pair F_2 = extension(B, H_2, P, A);

draw(A--P--B, lightblue);
draw(P--D, heavygreen);
draw(E_1--A--E_2, lightcyan);
draw(F_1--B--F_2, lightcyan);

pair X = extension(E_1, F_1, E_2, F_2);
pair C = 0.6*X+0.4*B;

filldraw(circle(midpoint(B--C), abs(B-C)/6), opacity(0.1)+brown, palered);
label("🦥", midpoint(B--C), fontsize(32pt));

draw(C--X, red);
draw(B--C, dotted+red);
draw(F_1--X, heavycyan);
draw(F_2--X, heavycyan);

dot("$P$", P, dir(P));
dot("$A$", A, dir(270));
dot("$B$", B, dir(270));
dot("$D$", D, dir(D));
dot("$E_1$", E_1, dir(45));
dot("$E_2$", E_2, dir(45));
dot("$F_1$", F_1, dir(135));
dot("$F_2$", F_2, dir(135));
dot("$X$", X, dir(270));
dot("$C$", C, dir(270));