M23-27

Question

The center of the circle is at point  (0, 6) . If the distance between the two points where the circle intersects the x-axis is 16, what is the area of the circle?

A.  36\pi  
B.  45\pi  
C.  64\pi  
D.  81\pi  
E.  100\pi

Bunuel · Answer

Official Solution:

The center of the circle is at point  (0, 6) . If the distance between the two points where the circle intersects the x-axis is 16, what is the area of the circle?

A.  36\pi  
B.  45\pi  
C.  64\pi  
D.  81\pi  
E.  100\pi

The radius of the circle  = \sqrt{6^2 + 8^2} = 10 . The area  = \pi10^2 = 100\pi .

Answer: E

filipTGIM · Answer

Or even more simple:

Identify that you have a 3-4-5 (6-8-10) triangle and without calculation you know that the hypothenuse is 10 => radius is 10.

Anonamy · Answer

I took the wrong approach with this question, would someone kindly clarify?

I had done a quick sketch of 0,6 on a graph and assumed that since the distance between the first point and where x meets the number line (x, 0) then the hypotenuse would be 16, and the radius would therefore be 16.

Where am I going wrong? I recognize that a 6-8-10 triangle can be formed from the side with a value of 6 however how does length 16 factor into this? Thanks

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=29121 The center of the circle is on y-axis, so it's symmetric around it. We know that the the distance between the two points where the circle intersects the x-axis is 16, hence half of it (8 units) must be to the left of 0 and the remaining half (another 8 units) to the right of 0. As you can see the radius of the circle is a hypotenuse of a right triangle with the sides equal to 6 and 16/2=8 (6-8-10 right triangle), so radius=hypotenuse=10. The area is \pi{r^2}=100\pi . Circle.png

Senthil7 · Answer

I think this is a  high-quality  question and I agree with explanation. Wow. This is a 700 level question certainly not 600 as classified by you Bunuel. Anyway terrific question in my view! Great work!

spetznaz · Answer

+1 for option E. Draw the graph , the answer will stand out almost immediately !

zishu912 · Answer

100pi

EgmatQuantExpert · Answer

Solution:

Given:

• Centre of the circle is at (6,0)

• The distance between points where the circle intersects the x-axis = 16 units

Working out: 
 
We need to find out the area of the circle.

To solve this problem, let us first draw a proper diagram. 
 
 https://e-gmat.com/blogs/wp-content/uploads/2018/03/Cap2.png 
The distance AB is 16 units (given in the question)

Since the diagram is symmetrical, AC=CB= AC/2 = 8 units.

OC = 6 units

Thus, AO (Radius of the circle) =  \sqrt{( 6^2 + 8^2)}  =  \sqrt{100}  = 10 units

Hence the area of the square =  pie * 10^2 = 100 pie

Answer: Option E

RenanBragion · Answer

I think this is a  high-quality  question and I agree with explanation.

Kali123 · Answer

Hi Bunuel,

Why should the diagram be symmtrical?

chetan2u · Answer

Because the center lies on y axis, that is y-axis acts as a diameter. The circle will be symmetrical about y-axis, as y-axis divide this circle in two parts

bumpbot · Answer

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M23-27

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