import solids;
import math;

size(10cm,0);
currentprojection=orthographic(-50,100,40);

//Draw right angle (MA,MB) in 3D
void drawrightangle(picture pic=currentpicture,
                    triple M, triple A, triple B,
                    real radius=0,
                    pen p=currentpen,
                    pen fillpen=nullpen,
                    projection P=currentprojection)
{
  p=linejoin(0)+linecap(0)+p;
  if (radius==0) radius=arrowfactor*sqrt(2);
  transform3 T=shift(-M);
  triple OA=radius/sqrt(2)*unit(T*A),
    OB=radius/sqrt(2)*unit(T*B),
    OC=OA+OB;
  path3 _p=OA--OC--OB;
  picture pic_;
    draw(pic_, _p, p=p);
    if (fillpen!=nullpen) fill(pic_, O--_p--cycle3, fillpen);
  add(pic,pic_,M);
}

// *...............Construction starts here................*

real r=1, h=.75;
real gle=60;
real gleA=20;
transform3 tR=rotate(gle,Z);
transform3 tT=shift((0,0,-h));

triple H=(0,0,h),//the label is O in the picture.
  A=rotate(gleA,Z)*(0,r,h),
  F=tR*A,
  B=tR*F,
  D=tT*A,
  C=tT*B,
  E=intersectionpoint(H--F,A--B);

revolution r=cylinder(O,r,h,Z);
// r.fill(white);
r.draw();

draw(O--H, dashed);
draw(O--D--C--cycle3^^O--H^^B--C, dashed);

drawrightangle(E,H,B,fillpen=black);

dot(Label("$O'$",align=NE+E), O);
layer();
fill(A--B--C--D--cycle3,lightgrey+opacity(.5));

dot(Label("$A$",align=NW), A);
dot(Label("$B$",align=N),B);
dot(Label("$C$",align=S), C);
dot(Label("$D$",align=NW), D);
dot(Label("$E$",align=S), E);
dot(Label("$F$",align=S), F);
dot(Label("$O$",align=N), H);

draw(H--B--F--A--cycle3^^H--F^^A--B^^A--D);

shipout(bbox(xmargin=10mm,invisible));