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Two tangents are drawn to the circle $C$, such that they meet each oth
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07 Aug 2025, 04:55
07 Aug 2025, 04:55
Expert Reply
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Question Stats:
36% (01:38) correct
63% (02:13) wrong based on 11 sessions
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Two tangents are drawn to the circle $C$, such that they meet each other at a point outside the circle making an angle of $x$ degrees. If the angle subtended by the two points of contact at the centre of the circle $C$ is $\(65^{\circ}\)$, what is $x$ ?
(A) 65
(B) 85
(C) 105
(C) 115
(E) 125
(A) 65
(B) 85
(C) 105
(C) 115
(E) 125
Re: Two tangents are drawn to the circle $C$, such that they meet each oth
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19 Aug 2025, 10:34
19 Aug 2025, 10:34
Expert Reply
Attachment:
GRE Two tangents are drawn.png [ 81.09 KiB | Viewed 60 times ]
In the figure above, two tangents $\(\mathrm{PA} \& \mathrm{~PB}\)$ intersect at point P and form an angle of x degrees. Also the angle formed at the centre is 65 degrees.
As radius is always perpendicular on tangent, we get angle $\(\mathrm{OBP}=\)$ angle $\(\mathrm{OAP}=90\)$ degrees each.
Now, in quadrilateral PAOB , we get angle $\(\mathrm{APB}=\mathrm{x}^{\circ}=360^{\circ}-\left(65^{\circ}+90^{\circ}+90^{\circ}\right)=360^{\circ}-245^{\circ}= 115^{\circ}\)$ (Sum of the angles of a quadrilateral is 360 degrees)
Hence the answer is (D).
gmatclubot
Re: Two tangents are drawn to the circle $C$, such that they meet each oth [#permalink]
19 Aug 2025, 10:34
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