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:

22

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°