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प्रश्न
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 ______.
विकल्प
20°
40°
35°
45°
उत्तर
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:
Given, AB ॥ PR
∴ ∠ABQ = ∠BQR = 70° ...[Alternate angles]
Also, QD is perpendicular to AB and QD bisects AB.
In ∆QDA and ∆QDB,
∠QDA = ∠QDB ...[90° each]
AD = BD
QD = QD ...[Common side]
∆ADQ ≅ ∆BDQ ...[By SAS congruency]
⇒ ∠QAD = ∠QBD [CPCT]...(i)
But ∠QBD = ∠ABQ = 70°
⇒ ∠QAD = 70° ...[From (i)]
Now, in ∆ABQ,
∠A + ∠B + ∠AQB = 180° ...[Angle sum property]
⇒ ∠AQB = 180° – (70° + 70°) = 40°
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