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°
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.
Related Questions
From a point which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is
60 cm2
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30 cm2
32.5 cm2
In the adjoining figure, PA and PB are tangents from point P to a circle with centre O. If the radius of the circle is 5 cm and PA ⊥ PB, then the length OP is equal to
5 cm
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5√2 cm
At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is
4 cm
5 cm
6 cm
8 cm
In the adjoining figure, if O is the centre of the circle then the value of x is
18°
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36°
