Multiple choice

In figure, if PA and PB are tangents to the circle with centre O such that $\angle$APB$=50^o$, then $\angle$OAB is equal to?

  1. $25^o$
  2. $30^o$
  3. $40^o$
  4. $50^o$
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A Correct answer
AI explanation

The sum of the angles in triangle APB is 180 degrees, so angle AOB equals 180 degrees minus 50 degrees, which is 130 degrees. In triangle AOB, the radii OA and OB are equal in length, making it an isosceles triangle with angle OAB equal to angle OBA. Therefore, angle OAB equals half of 180 degrees minus 130 degrees, which gives 25 degrees.

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