12.1.10 Olympic geometry

Problem: The circle \( \Omega \) with radius \( R=1 \) and two lines, intersecting at the angle \( \alpha=30^{\circ} \), were constructed on the plane, moreover, one of these lines passes through the centre of the circle \( \Omega \), the other one is tangent to the circle \( \Omega \). How many different circles are there on the plane, each of which is tangent to the circle \( \Omega \) and both mentioned lines?