Question

In the given figure, AB is the diameter. The tangent at C meets AB produced at Q.

If ∠ CAB = 34° , find : ∠ CQB

Answer 1

QC is tangent to the circle

∴ ∠ CAB  = ∠ QCB

Angle between tangent and chord = angle in alternate segment

∴ ∠ QCB =  34°

ABQ is a straight line

⇒ ∠ ABC + ∠ CBQ = 180°

⇒ 56° + ∠ CBQ = 180°

⇒ CBQ = 124°

Now,

∠ CQB  = 180° - ∠ QCB  = CBQ

⇒ ∠ CQB  = 180° - 34°- 124°

⇒ ∠ CQB   =  22°