(1) By similar triangles
OB
BC
 = 3
1
 so OB
OC
 = 3
4
 .
Again by similar triangles,
OA
OC
 = 2
3
 so OA
AC
 = 2
5
 .

The ratio
AB
OC
 = OB - OA
OC
 = 3
4
 - 2
5
 = 7
20
 .

(2) By similar triangles
OB
BC
 = 3
1
 so OB
OC
 = 3
4
 .
Again by similar triangles,
OA
OX
 = 4
3
where X is the midpoint of OC so
OA
OC
 = 4
14
 .

The ratio
AB
OC
 = OB - OA
OC
 = 3
4
 - 2
7
 = 13
28
 .

(3) This is exactly the same as (1) By similar triangles
OB
BC
 = 3
1
 so OB
OC
 = 3
4
 .
Again by similar triangles,
OA
OC
 = 2
3
 so OA
AC
 = 2
5
 .

The ratio
AB
OC
 = OB - OA
OC
 = 3
4
 - 2
5
 = 7
20
 .

Alternatively:
(1)
AB = 7
20
   __
Ö10
 

,
OC =   __
Ö10
 

.

(2)
AB = 13 Ö13
28

, OC = Ö13.

(3)
AB = 7Ö13
20

, OC = Ö13.