You will not succeed, because the constraints are not enough to pin the vertex C in one fixed place.Originally Posted by ragsk
Per the givens, point C is free to be anywhere on that ray (BC) of the known angle B---as long as point C does not coincide with point B.
If C is close to B, angle A will be small. As C goes away from B, the angle A becomes bigger. There are infinitely many answers as per the givens.
If the circle that you thought of has a known dimension---radius, diameter, circumference, coordinates of the center,....---then there will be only one answer. If the circle has no known dimension, then there are infinitely many answers.