Two tangents are drawn from an external point T to a circle with center O, touching at A and B. If ∠AOB = 120°, what is ∠ATB?

Solution

Solution: The radii OA and OB are perpendicular to the tangents at A and B. In quadrilateral AOBT, the angles at A and B are 90° each. Therefore, \(\angle ATB=360^\circ-90^\circ-90^\circ-120^\circ=60^\circ\). Trick: The angle between two tangents equals \(180^\circ\) minus the central angle between the radii to the points of contact.