What is the relation between x and y?
Consider the following for the next two (02) items that follow:<br>In the following figure, a triangle ABC is inscribed in a circle with centre at O. Let \angle POA=x^{\circ} and \angle OQB=y^{\circ}. Further, OB = BQ.
- A. x=y
- B. 2x=3y
- C. x=3y ✓
- D. 3x=4y
Correct Answer: C. x=3y
Explanation
Since OB=BQ, \triangle OBQ is isosceles, making \angle BOQ = y^{\circ}. The exterior angle \angle OBA = 2y^{\circ}. Since OA=OB, \angle OAB = 2y^{\circ}. The exterior angle \angle POA for \triangle OAQ is x^{\circ} = \angle OAQ + \angle OQA = 2y^{\circ} + y^{\circ} = 3y^{\circ}.
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