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 = 118°. Find the measure of ∠OCB.

59°

In quadrilateral ABCO

∠A + ∠B + ∠C + ∠O = 360º

[ ∠B = ∠C= 90º radius is perpendicular to tangent ]

118º + 90º + 90º + ∠O = 360º

∠O = 62º

In triangle OBC,

∠BOC + ∠OCB + ∠OBC = 180º

62º + ∠OCB + ∠OBC = 180º

[ ∠OCB = ∠OBC  angle made by equal sides are equal ]

 ∠OCB + ∠OBC = 180º - 62º

 2∠OCB = 118º

∠OCB = 59º