Multiple choice

The tangents at two points A and B on the circle with centre O intersect at P, if in quadrilateral PAOB, ?AOB : ?APB = 5 : 1. then measure of ?APB is -

  1. 15?

  2. 30?

  3. 45?

  4. 60?
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a quadrilateral formed by two tangents from an external point P and two radii to the points of tangency A and B, angle AOB (central angle) and angle APB (angle between tangents) are supplementary: angle AOB + angle APB = 180°. Given ratio 5:1, let angle AOB = 5x and angle APB = x. Then 5x + x = 180°, so 6x = 180°, x = 30°. Therefore angle APB = 30°.

Keep practicing — related questions