H2_pic5

import geometry;
import patterns;
size(9cm, 0);
defaultpen(fontsize(8pt));
dotfactor = 4;
point A,B,C,Ep,D,O;
A=origin; B=4*dir(75); C=4*dir(0); D=(A+C)/2;
line e = bisector(line(A,C), line(B,C));
Ep=intersectionpoint(e, line(A,B));
O=intersectionpoint(B--D, Ep--C);

markangle(radius=0.3cm,B,C,Ep);
markangle(radius=0.35cm,Ep,C,A);

add("diag", hatch(1mm, dir(45)));
fill(A--Ep--O--D--cycle, pattern("diag"));

draw(B--D^^Ep--C);

draw(A--B--C--cycle);

dot(A^^Ep^^B^^C^^D^^O);
label("$A$", A, S);
label("$B$", B, N);
label("$C$", C, S);
label("$D$", D, S);
label("$E$", Ep, WNW);
label("$O$", O, NE);
label(Label("$\frac{b}{2}$", Relative(0.5)), A--D);
label(Label("$\frac{b}{2}$", Relative(0.5)), D--C);
label(Label("$a$", Relative(0.5)), C--B);