AB is a diameter of the circle with centre O . The tangent at the point C on the circle meets AB produced at Q . If ∠BAC = 34°, then the measure of ∠CQA (in degrees) will be:
Answer & explanation
Correct answer: option 3
We know that,
∠BAC = 34°
Here, AO = CO = radius
∠OCQ = 90°
In triangle AOC,
∠OAC = ∠ACO = 34 [Angles opposite to equal sides]
= ∠COQ = ∠OAC + ∠ACO = 2 × 34° = 68° [External angle property]
In triangle CQO,
∠COQ + ∠OCQ + ∠CQO = 180°
= 68° + 90° + ∠CQO = 180°
= ∠CQO = 180° - 158° = 22°