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Question

Acute-angled ABC is inscribed in a circle with center at O; 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 OBE and BAC is:

Accepted Answer

FIGURE Because AB = 120^ and BC = 72^, AC = 168^. Also, OA = OC and OE AC, so AOE = COE = 84^. Since BOC = 72^, BOE = 156^. Finally, BOE is an isosceles triangle, so OBE = 12^. Because BAC = 12 72 = 36^, the ratio of the magnitudes of OBE and BAC is 1236 = 13, which is answer choice 13.