Circle through two points & tangent to an arc.

 From:  Frenchy Pilou (PILOU)
5513.2 In reply to 5513.1 
Rotate the circles A , B around the circle O by the center O
untill have line AB perpendicular to the vertical line OM (M is middle of AB)

You can now Draw your Circle by the 3 points ABC tangent in C! (C = Intersection OM and arc)
Make the rotation inverse if necessary for have the start position :)

EDITED: 30 Oct 2012 by PILOU