H2_pic8

import geometry;

size(9cm, 0);
defaultpen(fontsize(8pt));
dotfactor = 4;
point A,B,C,H,O1,O2,P,Q;
A=origin; B=5*dir(0);
circle circ = circle(A,B);
C=point(circ, 0.2*length(circ));
H=projection(A,B)*C;
circle circ1=circle(A,H);
circle circ2=circle(B,H);
O1=circ1.C;
O2=circ2.C;
point[] pc1=intersectionpoints(circ1, line(A,C));
P=pc1[1];

point[] pc2=intersectionpoints(circ2, line(C,B));
Q=pc2[1];
markrightangle(size=0.3cm, A, C, B);
markrightangle(size=0.3cm, A, P, H);
markrightangle(size=0.3cm, H, Q, B);
markrightangle(size=0.3cm, C, H, A);

draw(A--O1^^O1--H^^O1--P, white+opacity(0), StickIntervalMarker(1, 2, size=0.15cm));
draw(H--O2^^O2--Q^^O2--B, white+opacity(0), StickIntervalMarker(1, 1, size=0.15cm));

draw(C--H);
draw(P--O1^^P--H^^P--Q^^Q--O2^^Q--H);
draw(circ1^^circ2);
draw(A--B--C--cycle, black+pt);



dot(A^^B^^C^^H^^O1^^O2^^P^^Q);
label("A", A, W);
label("B", B, E);
label("C", C, N);
label(Label("H",UnFill), H, S);
label("$O_1$", O1, S);
label("$O_2$", O2, S);
label("P", P, N);
label("Q", Q, N);