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

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Manager
Joined: 06 Mar 2020
Posts: 90
Location: India
Concentration: Finance
GMAT 1: 660 Q48 V33
In the figure shown, O is the centre of the circle and PQ  [#permalink]

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08 Apr 2020, 07:36
1
3
00:00

Difficulty:

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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Screenshot 2020-04-08 at 9.03.26 PM.png [ 45.98 KiB | Viewed 481 times ]

Intern
Joined: 07 Apr 2020
Posts: 43
Re: In the figure shown, O is the centre of the circle and PQ  [#permalink]

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08 Apr 2020, 07:53
1
1
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,
$$∠PQO =90$$ , $$∠QPO = \frac{50}{2} = 25$$
$$∠PQO + ∠QPO + ∠QOP = 180$$
$$90 + 25 + ∠QOP = 180$$
$$∠QOP = 65$$
Senior Manager
Status: Studying 4Gmat
Joined: 02 Jan 2016
Posts: 350
Location: India
Concentration: Strategy, Entrepreneurship
GMAT 1: 590 Q37 V33
GPA: 4
WE: Law (Manufacturing)
Re: In the figure shown, O is the centre of the circle and PQ  [#permalink]

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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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Hero1kF

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Re: In the figure shown, O is the centre of the circle and PQ   [#permalink] 02 May 2020, 18:07