Multiple choice

AP and BP are tangents to circle with centre O at A and B respectively. If $\angle APB=80^{\circ}$, find $\angle AOB$

  1. $90^{\circ}$
  2. $100^{\circ}$
  3. $120^{\circ}$
  4. $150^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a quadrilateral formed by the center O and the tangents, the angles at the points of contact are 90 degrees. Thus, angle AOB + angle APB = 180 degrees. 180 - 80 = 100 degrees.

AI explanation

The radii to the points of tangency are perpendicular to the tangents AP and BP, making the angles OAP and OBP equal to 90 degrees each. In quadrilateral OAPB, the sum of all interior angles is 360 degrees, so angle AOB plus angle OAP plus angle OBP plus angle APB equals 360. Substituting the knowns gives angle AOB plus 90 plus 90 plus 80 equals 360, which simplifies to angle AOB plus 260 equals 360. Solving this yields angle AOB equals 100 degrees.

Keep practicing — related questions