Answer
We know that when a line starting at the center of a circle intersects an arc, it bisects the arc. Now, we must consider congruent triangles. OB is congruent to itself by the identity property, and it is given that ON is congruent to OM. Since they are right triangles, this means that the other sides, MB and NS, are also congruent. Since these are both bisected, this means that AB and CB are congruent. Since AB and CB are congruent, it follows that ABC is isosceles.
