Multiple choice

In figure, if PA and PB are tangents to circle with centre O such that $\angle APB=80^{\circ}$, then $\angle OAB$ is equal to:

  1. $25^{\circ}$
  2. $30^{\circ}$
  3. $40^{\circ}$
  4. $50^{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In quadrilateral OAPB, angles at A and B are 90 degrees. Angle APB = 80. Angle AOB = 180 - 80 = 100 degrees. Triangle OAB is isosceles with OA = OB. Angle OAB = (180 - 100) / 2 = 40 degrees.

AI explanation

Since PA and PB are tangents from an external point P, triangle OAP is a right triangle where angle OAP is 90 degrees. In triangle OAPB, the two right triangles OAP and OBP are congruent, making angle OAB exactly half of angle OABP. Because the sum of angles in quadrilateral OAPB dictates angle AOB is 100 degrees, angle OAB equals 40 degrees.

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