import geometry;

size(9cm, 0);
defaultpen(fontsize(10pt));
dotfactor = 4;

point A,B,B1,O,C;

B=(0,0); B1=-2*dir(80);
circle circ = circle(B, B1);
O=circ.C;
C=point(circ, -1/15*length(circ));
A=point(circ, B-1/4*length(circ)); //не смог придумать решени, как от точки B отступить дугу 90

fill(A--O--B--cycle, red+white);
fill(C--O--B--cycle, blue+white);
fill(A--O--C--B1--cycle, orange+white);

markangle(Label("$\alpha$", Relative(0.5), align = NE), radius = 0.3cm, n=1, C,O,B);
markrightangle(size=0.2cm, B,O,A);
draw(B--B1);
draw(B--C^^O--C^^O--A^^A--B);
draw(circ);


pair p []={A, B, B1, C, O};
pair v []={W, N, S, SE, SW};
string n []={"$A$", "$B$", "$B_1$", "$C$", "$O$"};

for ( int k=0; k<p.length ; ++k)
dot ( Label (n[k] , align =v[k]) ,p[k ]);

label(Label("$1$", Relative(0.5)), A--O);
label(Label("$1$", Relative(0.5)), B--O);
label(Label("$1$", Relative(0.5)), C--O);
label(Label("$\sqrt2$", Relative(0.5), Rotate(dir(A--B)), align = N), A--B);
label(Label("$\frac{10}3$", Relative(0.5), Rotate(dir(B--C)), align = NE), B--C);
label("$S_1$", (A+O+B)/3);
label("$S_2$", (C+O+B)/3);
label("$S_3$", (3*A+3*O+C)/6);