Multiple choice

If PA and PB are tangents to the circle with centre O such that ∠APB = 50o. Then ∠OAB =?

  1. 25o

  2. 30o

  3. 40o

  4. 70o
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

PA and PB are tangents from point P to circle with center O. Tangents from a point to a circle are equal in length, so PA = PB. In isosceles triangle APB with apex angle ∠APB = 50°, the base angles are equal: ∠PAB = ∠PBA = (180° - 50°)/2 = 65°. Since OA is radius and PA is tangent, OA ⟂ PA, so ∠OAP = 90°. Therefore, ∠OAB = ∠OAP - ∠PAB = 90° - 65° = 25°. This matches option A. The claimed answer is correct.

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