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In the diagram above CD is a tangent to the circle with center O at A.
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05 Dec 2023, 01:39
05 Dec 2023, 01:39
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49% (01:35) correct
49% (01:07) wrong based on 14 sessions
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GRE In the diagram above CD.jpg [ 15.5 KiB | Viewed 2440 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.
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Re: In the diagram above CD is a tangent to the circle with center O at A.
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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.
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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.
