AB is a diameter of the cirlce with centre O. The tangent at the point C on the cirlce meets AB produced at Q. If BAC = 34º , then the measure of CQA (in degrees) will be:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 22.
AO = CO = radius
∠OCQ = 90° [A tangent is perpendicular to the radius at the point of tangency]
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° [∵Property of Angle sum]
⇒ 68° + 90° + ∠CQO = 180°
⇒ ∠CQO = 180° - 158° = 22°
∠CQA = ∠CQO = 22°
Hence ∠CQA is 22°.