From a point $P$ , two tangents are drawn to a circle whose centre is $O$ , touching the circle at $Q$ and $R$ . If $∠$ $Q O R$ is $120$ $^{\circ}$ , $∠$ $Q P R$ is -

40

^{\circ}

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45

^{\circ}

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50

^{\circ}

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60

^{\circ}

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Solution

The correct option is D $60$ $^{\circ}$
In the quadrilateral $O Q P R, ∠ O Q P = ∠ O R P = 90^{o}$ since tangent is perpendicular to radius at the point of contact.
By the angle sum property then, we have:
$∠ Q P R = 360 - 90 - 90 - 120 = 60^{o}$
So option D is the right answer.

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From a point P, two tangents are drawn to a circle whose centre is O, touching the circle at Q and R. If ∠ QOR is 120 ∘, ∠ QPR is -

The correct option is D 60 ∘In the quadrilateral OQPR, ∠OQP=∠ORP=90o since tangent is perpendicular to radius at the point of contact.By the angle sum property then, we have:∠QPR=360−90−90−120=60oSo option D is the right answer.

From a point $P$ , two tangents are drawn to a circle whose centre is $O$ , touching the circle at $Q$ and $R$ . If $∠$ $Q O R$ is $120$ $^{\circ}$ , $∠$ $Q P R$ is -

The correct option is D $60$ $^{\circ}$
In the quadrilateral $O Q P R, ∠ O Q P = ∠ O R P = 90^{o}$ since tangent is perpendicular to radius at the point of contact.
By the angle sum property then, we have:
$∠ Q P R = 360 - 90 - 90 - 120 = 60^{o}$
So option D is the right answer.