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# In the diagram above, O is the center of the circle. What is the leng

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In the diagram above, O is the center of the circle. What is the leng  [#permalink]

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11 Mar 2015, 04:47
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In the diagram above, O is the center of the circle. What is the length of chord AC?

(1) chord BC = 14
(2) the circle has an area of $$625\pi$$

Kudos for a correct solution.

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Re: In the diagram above, O is the center of the circle. What is the leng  [#permalink]

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11 Mar 2015, 06:03
1
the answer is C

from the question we know that AB is the diameter and the tringle ACB is right tringle 90-60-30

statment 1 insuff where we can not find AC with no information about the other side AB
statment 2 insuff it allow us just to find AB=50 where no information about other side CB
from 1&2 we have AB&CB so we can find AC
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Re: In the diagram above, O is the center of the circle. What is the leng  [#permalink]

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11 Mar 2015, 07:05
Answer should be C.
triangle ABC is right angled triangle, as angle made by diameter on a triangle is right angle.
We need any two sides to get the third side`s length.
statement 1 is not sufficient, so is the statement 2.
considering 1 + 2 , We can get the diameter of the circle from 2, which is one side of the triangle and from 1 we have another side.
So, by Pythagoras theorem, we can get length of AC. Sufficient.
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Re: In the diagram above, O is the center of the circle. What is the leng  [#permalink]

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11 Mar 2015, 10:59
Hi

Statement i >> insufficient
We don't know the radius.

Statement ii >> insufficient
We don't know the length of the other two chords, we just can calculate the diameter

Statement i + ii >> sufficient

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Re: In the diagram above, O is the center of the circle. What is the leng  [#permalink]

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11 Mar 2015, 19:10
Bunuel wrote:
Attachment:
cpotg_img4-300x285.png
In the diagram above, O is the center of the circle. What is the length of chord AC?

(1) chord BC = 14
(2) the circle has an area of $$625\pi$$

Kudos for a correct solution.

The triangle formed is a right triangle, we just need to figure out 2 of the sides.

Statement 1: Only 1 side is given
Insufficient

Statement 2: Only 1 side is given
Insufficient

Combined, we have 2 sides and can use pythagorean theorem.
Sufficient

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Posts: 49320
Re: In the diagram above, O is the center of the circle. What is the leng  [#permalink]

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15 Mar 2015, 22:51
Bunuel wrote:

In the diagram above, O is the center of the circle. What is the length of chord AC?

(1) chord BC = 14
(2) the circle has an area of $$625\pi$$

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

The fact that AB is a diameter guarantees that angle C = 90º. If we had two sides of right triangle ABC, we could find the third using the Pythagorean Theorem.

Statement #1: this gives us only one side of a right triangle: not helpful. This statement, alone and by itself, is not sufficient.

Statement #2: this allows us to solve for the radius and, hence, the diameter, so we can determine side AB. Nevertheless, this gives us only one side of a right triangle: also not helpful. This statement, alone and by itself, is not sufficient.

Combined statements: We get the length of BC from the first statement, and the length of AB from the second. Now, we have two sides of the right triangle, so we can use the Pythagorean Theorem to solve for the third side, AC. Combined, the statements are sufficient.

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Re: In the diagram above, O is the center of the circle. What is the leng  [#permalink]

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15 Apr 2017, 17:24
23a2012 wrote:
the answer is C

from the question we know that AB is the diameter and the tringle ACB is right tringle 90-60-30

statment 1 insuff where we can not find AC with no information about the other side AB
statment 2 insuff it allow us just to find AB=50 where no information about other side CB
from 1&2 we have AB&CB so we can find AC

Don't think you can assume it's a 30-60-90 triangle. Flawed reasoning here.
Re: In the diagram above, O is the center of the circle. What is the leng &nbs [#permalink] 15 Apr 2017, 17:24
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# In the diagram above, O is the center of the circle. What is the leng

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