1. In triangle ABC, the circumcenter is O; points A and B, C lie on opposite sides of the center. If \(\angle BOC = 120^\circ\), then what is the measure of \(\angle BAC\)?

(a) 50° (b) 60° (c) 70° (d) 80°

2. O is the circumcenter of triangle ABC. If \(\angle\)BAC = 85° and \(\angle\)BCA = 70°, then what is the measure of \(\angle\)OAC?

(a) \(65^o\) (b) \(42\cfrac{1}{2}^o\) (c) \(50^o\) (d) \(25^o\)

3. In triangle ABC, the circumcenter is O. If \(\angle\)BAC = 85° and \(\angle\)BCA = 75°, then what is the measure of \(\angle\)OAC?

(a) 70° (b) 40° (c) 110° (d) 140°

4. If the orthocenter, centroid, circumcenter, and incenter of a triangle all lie at the same point, then what type of triangle is it?

(a) isosceles (b) scalene (c) equilateral (d) right-angled isosceles

5. In triangle \(\triangle ABC\), O is the circumcenter. If \(\angle OAB = 35^\circ\), then what is the measure of \(\angle ACB\)?

(a) 45° (b) 50° (c) 55° (d) 60°

6. In triangle ABC, the circumcenter is \(O\). If \(\angle\)BAC = 85° and \(\angle\)BCA = 75°, then what is the measure of \(\angle\)AOC?