From an external point P, two tangents PA and PB are drawn to a circle with centre O, touching it at A and B. If angle APB = 70°, what is the measure of angle OAB?

Radii are perpendicular to tangents, so angle OAP = angle OBP = 90°. In quadrilateral OAPB, angle AOB = 360° − 90° − 90° − 70° = 110°. Triangle OAB is isosceles (OA = OB), so angle OAB = (180° − 110°)/2 = 35°.