AB is a diameter of a circle with centre O. The tangent at a point C on the circle meets AB produced at Q. If ∠CAB = 42°, then what is the measure of ∠CBA ?
Answer & explanation
Correct answer: option 3
OA and OC are radius of circle.
⇒ ∠QAC = ∠QCA = 42º
OC is radius of circle and form 90º angle at tangent QC.
∠QOC is exterior angle of triangle ACO .
So, ∠QOC = ∠QAC + ∠QCA
= 42º + 42º
= 84º
In triangle CAQ,
∠CAQ + ∠CQA + ∠QCA = 180º
42º + 90º + ∠CQA = 180º
∠CQA = 48º