GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Two tangents are drawn to the circle $C$, such that they meet each oth
[#permalink]
07 Aug 2025, 04:55
07 Aug 2025, 04:55
Expert Reply
00:00
Question Stats:
30% (01:22) correct
69% (02:01) wrong based on 13 sessions
Hide Show timer Statistics
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
(D) 115
(E) 125
(A) 65
(B) 85
(C) 105
(D) 115
(E) 125
Re: Two tangents are drawn to the circle $C$, such that they meet each oth
[#permalink]
19 Aug 2025, 10:34
19 Aug 2025, 10:34
Expert Reply
Attachment:
GRE Two tangents are drawn.png [ 81.09 KiB | Viewed 760 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
Moderators:
