Problem: Acute-angled triangle ABC is inscribed in a circle with center at O, and AB=120∘ and BC=72∘. A point E is taken in minor arc AC such that OE is perpendicular to AC. Then the ratio of the magnitudes of angles OBE and BAC is:
Answer Choices:
A. 185
B. 92
C. 41
D. 31
E. 94
Solution:
The magnitude of angle BOE is 156∘. Therefore, the magnitude of angle OBE=21(180∘−156∘)=12∘. Since the magnitude of angle BAC=36∘, the required ratio is 3612 or 31.