Question

In figure, if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and ∠BQR = 70°, then ∠AQB is equal to ______ 

 

Options

• 20°

• 40°

• 35°

• 45°

Answer 1

In figure, if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and ∠BQR = 70°, then ∠AQB is equal to 40°.

Explanation:

AB || PR

∴ ∠ABQ =∠BQR  ........[Alternate interior angles]

⇒ ∠ABQ = 70°

Also, ∠BQR = ∠BAQ  .......[Angles in alternate segment]

⇒ ∠BAQ = 70°

In ∆AQB,

∠BAQ + ∠ABQ + ∠AQB = 180°

⇒ 70° + 70° + ∠AQB = 180°

⇒ ∠AQB = 180° – 140° = 40°.