AB and AC are tangents to a circle with centre O from an external point A. The tangents AB and AC touch the circle at B and C respectively, such that BAC = 118º. Find the measure of OCB.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 59º
∠BAC + ∠ACO + ∠ABO + ∠COB = 360° (since ABCO is a quadrilateral)
⇒ 118° + 90° + 90° + ∠COB = 360° (∠ACO = ∠ABO = 90° tangent makes 90° with the radius of circle)
⇒ ∠COB = 360° - 298° = 62°
In ∆OCB
∠ COB + ∠OCB + ∠OBC = 180°
⇒ 62°+ 2∠OCB = 180° (∠OCB = ∠OBC or OC = OB (radius)}
⇒ 2∠ OCB = 118°
⇒ ∠OCB = 59°