have gotten a bit closer now, i post my try in the hope someone can spot an error or finish the problem
i have joined C to O, centre of hemisphere so A0=0B=OC=a. this gives some isoc trinagle which lead to ACB=90,ABC=60.
Tsin 30+Tsin 60=w
sin 60=AC/2a so AC=art(3) hence extension is art(3)-4a/3=a(21rt(3)-28)/21
cos 60=BC/2a so BC=a hence extension is a-4a/7=a(21-12)/21=9a/21
giving total extension a[21rt(3)-28+9]/21=a[rt(3)-1]
which is close but no cigar. How can i rid myself of the 29/21?