Mathematics
In the adjoining figure, PQ and PR are tangents from P to a circle with centre O. If ∠POR = 55°, then ∠QPR is
35°
55°
70°
80°
Circles
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Answer
OR ⊥ PR (∵ radius of a circle and tangent through that point are perpendicular to each other.)
∴ ∠ORP = 90°.
Since, sum of angles in a triangle = 180°.
⇒ ∠ORP + ∠POR + ∠OPR = 180°
⇒ 90° + 55° + ∠OPR = 180°
⇒ 145° + ∠OPR = 180°
⇒ ∠OPR = 180° - 145°
⇒ ∠OPR = 35°.
∠QPO = ∠OPR = 35° (∵ the tangents are equally inclined to the line joining the point and the centre of the circle.)
From figure,
∠QPR = ∠OPR + ∠QPO = 35° + 35° = 70°.
Hence, Option 3 is the correct option.
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