Multiple choice

In a circle with centre O, PA and PB are the tangents at A and B, respectively, from an external point P. If ∠APB = 42°, then what will be the measure of ∠AOB?

  1. 159°

  2. 142°

  3. 121°

  4. 138°

  5. NA
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D Correct answer
Explanation

In quadrilateral OAPB, angles at A and B are 90 degrees. Sum of angles is 360. Angle AOB = 180 - Angle APB = 180 - 42 = 138.

AI explanation

The radius is perpendicular to the tangent at the point of contact, so angles OAP and OBP are 90 degrees each. In quadrilateral OAPB, the sum of all interior angles is 360 degrees. We have 90 degrees plus 90 degrees plus 42 degrees plus angle AOB equals 360 degrees. Solving this gives angle AOB equals 360 degrees minus 222 degrees, which is 138 degrees.

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