What is \angle AQP equal to?

Consider the following for the next two (02) items that follow: AB is a diameter of a circle with centre O. Radius OP is perpendicular to AB. Let Q be any point on arc PB.

  1. A. 30^{\circ}
  2. B. 40^{\circ}
  3. C. 45^{\circ}
  4. D. 60^{\circ}

Correct Answer: C. 45^{\circ}

Explanation

The angle subtended by an arc at the center is double the angle it subtends at any point on the remaining part of the circle. Arc AP subtends \angle AOP = 90^{\circ} at the center. Therefore, the angle it subtends at Q on the circumference is \angle AQP = \frac{90^{\circ}}{2} = 45^{\circ}.

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