And it is manifest that,
when the center of the circle falls within the triangle,
the angle BAC, being in a segment greater than the semicircle, is less than a right angle;
when the center falls on the straight line BC,
the angle BAC, being in a semicircle, is right;
and
when the center of the circle falls outside the triangle,
the angle BAC, being in a segment less than the semicircle, is greater than a right angle. [III.31]

