The verticals of ΔABC lie on a circle with center O. TC is a tangent to the circle at the point C.  If BC bisects the ∠OCT, then what is the measure of ∠CAB?

90° 135° 45° 100°

45°

Tangent property :  ∠BCT = ∠BAC = x and ∠OBC = ∠OCB = x             (radius) ∠BOC = 2 × ∠A = 2x In ΔOBC,sum of angles = 180° ⇒ 2x + x + x = 180° ⇒ 4x = 180° ⇒ x = 45°