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

Question

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 .

23a2012 · Answer

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

aniteshgmat1101 · Answer

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.

iamdp · Answer

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

Answer C

peachfuzz · Answer

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

Answer: C

Bunuel · Answer

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.

Answer = (C)

Cez005 · Answer

Don't think you can assume it's a 30-60-90 triangle. Flawed reasoning here.

BrentGMATPrepNow · Answer

Target question :    What is the length of chord AC?

Given : O is the center of the circle  
If O is the center of the circle, then AB is the circle's DIAMETER 
If AB is the DIAMETER, then ∠C = 90°, because ∠C is an inscribed angle containing ("holding") the diameter. 
So, let's first add this information to the diagram 
 https://i.imgur.com/MI5itDc.png

Statement 1 : chord BC = 14  
Notice that the length of chord BC has no bearing on the length of chord AC. 
In fact, here are two diagrams that satisfy statement 1: 
 https://i.imgur.com/H0xeWiX.png

In the left-hand diagram, the answer to the target question is  chord AC has length 20 
In the right-hand diagram, the answer to the target question is  chord AC has length 30 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : the circle has an area of 625π 
 Area of circle = πr² 
So, we can write: πr² = 625π
Divide both sides by π to get: r² = 625
Solve: r = 25
So, the circle's radius = 25, which means the DIAMETER AB has length 50.

This time the length of the diameter has little bearing on the length of chord AC. 
In fact, here are two diagrams that satisfy statement 2: 
 https://i.imgur.com/1Y4zmIH.png

In the left-hand diagram, the answer to the target question is  chord AC has length 30 
In the right-hand diagram, the answer to the target question is  chord AC has length 40 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
When we combine the two statements, we see that we know the lengths of two sides of a RIGHT triangle
 https://i.imgur.com/x6323MZ.png

So, we COULD apply the Pythagorean Theorem to write: 14² + x² = 50², 
And we COULD solve the equation to get  x = 48 . 
However, performing all of those calculations would be a waste of the time, since we need only show that we COULD answer the  target question  with certainty.
Since we COULD answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

RELATED VIDEO 
 https://www.youtube.com/watch?v=xiyv2MacIUk

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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

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