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.
In the diagram above CD is a tangent to the circle with center O at A.
[#permalink]
05 Dec 2023, 01:39
05 Dec 2023, 01:39
Expert Reply
00:00
Question Stats:
54% (01:43) correct
45% (00:58) wrong based on 11 sessions
Hide Show timer Statistics
Attachment:
GRE In the diagram above CD.jpg [ 15.5 KiB | Viewed 853 times ]
In the diagram above CD is a tangent to the circle with center O at A.
Quantity A |
Quantity B |
Length of EO |
\(6 \sqrt{3}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Part of the project: The Butler-GRE Daily New Quant and Verbal Questions to Practice (2023) - Gain 20 Kudos & Get FREE Access to GRE Prep Club TESTS
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
Manager
Joined: 11 Nov 2023
Posts: 207
Given Kudos: 76
WE:Business Development (Advertising and PR)
Re: In the diagram above CD is a tangent to the circle with center O at A.
[#permalink]
06 Dec 2023, 10:23
06 Dec 2023, 10:23
1
We can see angle OAE is 90°, since a tangent is perpendicular to the radius of the circle. Thus, △OAE is a 30°-60°-90° triangle and the ratios of the sides are \(x:x\sqrt{3}:2x\).
Since we're given that the side opposite the 30° is 6, we know the side opposite the 90°, which is EO, is 12, which is greater than \(6\sqrt{3}\).
Since we're given that the side opposite the 30° is 6, we know the side opposite the 90°, which is EO, is 12, which is greater than \(6\sqrt{3}\).
In the diagram above CD is a tangent to the circle with center O at A.
[#permalink]
29 Jan 2024, 21:51
29 Jan 2024, 21:51
1
Since CD is tangent to the circle at A \(\angle EAO \) will be 90 degrees.
Since \(\angle EOA\) is 60 degrees, \(\angle AEO\) will be 30 degrees.
This gives us a \(30-60-90\) triangle. The sides of such a triangle are in the ratio \(x:\sqrt{3}x:2x\)
Now \(EO\) is the hypotenuse and is the longest side, since it is opposite to the 90 degree angle. Its length is given by \(2x\). We know \(x=6\) since it is opposite to the shortest angle, 30 degrees.
Therefore the length of EO will be \(6 \times 2 = 12\)
Quantity A = \(12\)
Quantity B = \(6\sqrt{3}\) (this is actually the value of EA, and is a trap)
Quantity A is the greatest.
Since \(\angle EOA\) is 60 degrees, \(\angle AEO\) will be 30 degrees.
This gives us a \(30-60-90\) triangle. The sides of such a triangle are in the ratio \(x:\sqrt{3}x:2x\)
Now \(EO\) is the hypotenuse and is the longest side, since it is opposite to the 90 degree angle. Its length is given by \(2x\). We know \(x=6\) since it is opposite to the shortest angle, 30 degrees.
Therefore the length of EO will be \(6 \times 2 = 12\)
Quantity A = \(12\)
Quantity B = \(6\sqrt{3}\) (this is actually the value of EA, and is a trap)
Quantity A is the greatest.
