In the given figure, O is the center of the circle. If AB = OC, then what is the ratio of ∠CAO to the ∠DOC ?
Answer & explanation
Correct answer: option 4
OC = AB
OC = OB = r
∠OBC = θ + θ = 2θ (exterior angle)
∠OBC = ∠OCB = 2θ (angle opposite to equal side area)
∠BOC = 180° - 4θ
∠DOC = 180° - (180° - 4θ + θ) = 3θ
\(\frac{∠CAO}{∠DOC}\) = \(\frac{θ}{3θ}\) = \(\frac{1}{3}\)