If the three identical circles shown are centered at K, L, and M, resp

Question

https://gmatclub.com/forum/download/file.php?id=51139 If the three identical circles shown are centered at K, L, and M, respectively, and all are tangent to one another, what is the area of the triangle shown in the figure? (1) Triangle KLM is an equilateral triangle. (2) The radius of circle K is 3. image020 (1).jpg

chetan2u · Answer

Since the circles are tangent to each other, when we join the centers,  each side will be twice the radius ..
Thus, what we have is  an equilateral triangle with side 2r . The area will be  {\frac{\sqrt{3}}{4}}*\pi*r^2 .
So, the question finally becomes --  What is radius?

(1) Triangle KLM is an equilateral triangle.
 We already know it

(2) The radius of circle K is 3.
We have the radius..
Suff

B

93soni · Answer

As given in question three identical circles => radius of 3 circle will be same.
Let it be r => triangle will be equilateral with side as 2r.

Now statement 1)
Already know what is given in this statement therefore not sufficient

Now statement 2)
r =3
=> area of equilateral triangle will be sqrt(3)× r^2

Therefore sufficient B

Posted from my mobile device

EgmatQuantExpert · Answer

Solution

Step 1- Given and To find

Given 
 • Three identical circles shown are centered at K, L, and M.
• All the circles are tangent to each other.

To find 
 • Area of triangle

All three circles are identical.
 • Half of each side of the triangle is radius of the circle.
 o Hence, all three sides are equal. 
  Therefore, the triangle is equilateral. 
o And, the side length is 2× Radius of each circle.

To find the area of the triangle, we will need the side of triangle. And, to find side, we need radius of the circle.
 • Therefore, to find the answer, we only need radius of the circle.

Step 2: Analysing individual statements

Statement 1:   Triangle KLM is an equilateral triangle.

This does not give us any information about the radius of the circle. 
Hence, this statement is not sufficient.

Statement 2:   The radius of circle K is 3.

We have the radius of the circle. 
Hence, we can find the answer from this statement.

Thus, option B is the correct answer.
  Correct Answer: Option B

chrtpmdr · Answer

What does it mean that all are tangent to each other?

bumpbot · Answer

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If the three identical circles shown are centered at K, L, and M, resp

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If the three identical circles shown are centered at K, L, and M, resp

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