#### Question

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

If ∠CAB = 34°, Find:

(i)∠CBA (ii) ∠CQB

#### Solution

i) AB is diameter of circle.

∴ ACB = 90°

In ΔABC,

`∠`A + B + `∠`C = 180°

⇒ 34° + `∠`CBA + 90° = 180°

⇒ `∠`CBA = 56°

ii) 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°

Is there an error in this question or solution?

Solution In the Given Figure, Ab is the Diameter. the Tangent at C Meets Ab Produced at Q. If ∠Cab = 34°, Find: (I)∠Cba (Ii) ∠Cqb Concept: Chord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord.