A) So pick an arbitrary point, $A$, on the circle and draw the tangent. Now pick a line perpendicular to the tangent, the intersections of this line and the circle will be $B,C$. We need to prove that one of the arcs is between 180 and 270. If $C$ is further away from $A$, then it is clear that major arc $AC$ follows these conditions. B) It's pretty clear that the triangle must be isoceles. Say the congruent angles are $A$ and $B$ on a circle. Then $C$ is on the midpoint of minor arc $AB$. And the line through $B$ and $C$ is perpendicular to the tangent at $A$ (vice versa for $B$ because of symmetry). After some angle chasing, we get the angle between the tangents at $A$ and $B$ is $60^\circ$, so the angles are $120,30,30$