H3_pic2

import geometry;

size(9cm, 0);
defaultpen(fontsize(10pt));
dotfactor = 6;
point A,B,C,O,B1,O1,C1;
real r=2;
real R=2*r;
O=origin; A=-2r*dir(30);
O1=O+R*dir(A--O);

circle circ1=circle(O, r);
line[] t=tangents(circ1, A);
point[] Bp=intersectionpoints(circ1,t[0]);
B=Bp[0];
point[] Bp=intersectionpoints(circ1,t[1]);
B1=Bp[0];

circle circ2=circle(O1,R);
line[] tt=tangents(circ2, A);
point[] Cp=intersectionpoints(circ2,tt[0]);
C=Cp[0];
point[] Cp=intersectionpoints(circ2,tt[1]);
C1=Cp[0];
point F = projection(O1,C)*O;

markangle(Label("$30^\circ$"),radius=0.5cm, C,A,O);
markangle(Label("$30^\circ$"),radius=0.4cm, O,A,B1);
markangle(Label("$30^\circ$"),radius=0.5cm, F,O,O1);
markrightangle(size=0.3cm,O1,F,O);
markrightangle(size=0.3cm,O1,C,B);
markrightangle(size=0.3cm,O,B,A);
draw(circ1^^circ2);
label(Label("$R$", Rotate(dir(O--O1))), O1--O, UnFill);
draw(O--B^^O1--C^^O--F);
draw(A--(C+dir(A--C))^^A--(C1+2*dir(A--C1))^^A--(O1+5*dir(A--O1)));

dot(A^^B^^B1^^O^^O1^^C^^C1^^F);

label("$A$",A,S);
label("$B$",B,S);
label("$C$",C,S);
label("$O$",O,WNW);
label("$O_1$",O1,N);
label("$F$",F,E);
label(Label("$r$"),O--B);
label(Label("$r$"),C--F);
label(Label("$R-r$"),F--O1);