Multiple choice

In a circle with centre O, PAX and PBY are the tangents to the circle at points A and B, from an external point P. Q is any point on the circle such that (\angle QAX = 59°) and (\angle QBY = 72°). What is the measure of (\angle AQB)?

  1. $72°$
  2. $49°$
  3. $59°$
  4. $31°$
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B Correct answer
Explanation

Since PA and PB are tangents from point P, PA = PB and OA ⟂ PA, OB ⟂ PB. Angle between tangent and chord equals angle in the alternate segment. Therefore, angle QAX = angle AQP = 59° and angle QBY = angle BQP = 72°. In triangle AQB, angle AQB = 180° - (59° + 72°) = 49°.

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