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?
Answer & explanation
Correct answer: option 3
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°