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Source: — Problem Solving |

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by [email protected] » Tue Jun 03, 2014 12:47 am
Hi shibsriz,

I'm going to give you a couple of hints and let you attempt this question again:

1) To calculate the perimeter of triangle ABE, you'll NEED some actual numbers to work with.
2) Draw a picture with a radius running from the center of the circle to point A and another running to point B. With the knowledge that arc AB = 120 degrees, what do you know about arc AE and arc BE (hint: how many degrees are in a circle)?

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by theCodeToGMAT » Tue Jun 03, 2014 12:55 am
{C}?
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by sukriti2hats » Tue Jun 03, 2014 1:54 am
Let the centre of the circle be O.

AO=BO=EO because they represent the radius.

Statement 1- measure of arc AB is 120 degrees.

The angle AOB is 120. The angles AOE and BOE will also be equal to 120. So the measure of arc AE = BE =120.
In triangles AOB , AOE and BOE, sides AO=BO=EO because they are radii and angle AOB=BOE=AOE=120 degrees. So by side-angle -side condition these three triangles are congruent. Thus the sides of the triangle, AB =AE=BE. It is an equilateral triangle.
But as Rich said, in order to find out the perimeter we need actual numbers to work with, statement 1 is Insufficient.

Statement 2- AB is 2 units

Knowing the length of AB alone will not help in finding the perimeter of the triangle.
So statement 2 is also Insufficient.

Togther using 1 and 2, we can find out by 1 that triangle is equilateral and then by using the information that AB=2 we can find out the perimeter i.e. AB+BE+AE= 2+2+2=6
So the correct answer is C.
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