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In the figure shown, O is the centre of the circle and PQ

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In the figure shown, O is the centre of the circle and PQ  [#permalink]

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New post 08 Apr 2020, 07:36
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  25% (medium)

Question Stats:

76% (01:50) correct 24% (01:46) wrong based on 51 sessions

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In the figure shown, O is the centre of the circle and PQ, PR and ST are tangents. What is the angle QOP?


A) 40 degrees
B) 45 degrees
C) 65 degrees
D) 75 degrees
E) 90 degrees

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Re: In the figure shown, O is the centre of the circle and PQ  [#permalink]

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New post 08 Apr 2020, 07:53
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770GMAT wrote:
In the figure shown, O is the centre of the circle and PQ, PR and ST are tangents. What is the angle QOP?


A) 40 degrees
B) 45 degrees
C) 65 degrees
D) 75 degrees
E) 90 degrees


Solution:


By the properties of triangle
    PQ = PR …Tangent to the circle from same point outside the circle.
    \(∠PQO = ∠PRO = 90\)… The point where tangent is touching the circle makes an angle of 90 to the centre of the circle.
Draw a line PO.
    Triangle PQO is congruent to triangle PRO
    In triangle PQO,
      \(∠PQO =90\) , \(∠QPO = \frac{50}{2} = 25\)
      \(∠PQO + ∠QPO + ∠QOP = 180\)
      \(90 + 25 + ∠QOP = 180\)
      \(∠QOP = 65\)
Answer: Option C.
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Re: In the figure shown, O is the centre of the circle and PQ  [#permalink]

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New post 02 May 2020, 18:07
The Degree of Minor Arc + The Angle outside formed by intersecting tangent = 180 Degree.
Hence, QOR is 130, and when a middle line is drawn from O to P its bisects the angle. Hence 65 is answer.
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Re: In the figure shown, O is the centre of the circle and PQ   [#permalink] 02 May 2020, 18:07

In the figure shown, O is the centre of the circle and PQ

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