Advertisement Remove all ads

Advertisement Remove all ads

Advertisement Remove all ads

MCQ

Fill in the Blanks

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°

Advertisement Remove all ads

#### Solution

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°.

Concept: Tangent to a Circle

Is there an error in this question or solution?