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.
Answer & explanation
Correct answer: option 1
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