In the xy-plane, the center of a circle is located at (8, 11). The

Question

In the xy-plane, the center of a circle is located at (−8, −11). The point (−8, −8) lies inside the circle, and the point (−11, −7) lies outside the circle. If the circle’s radius is an integer, what is its area?

A. 4π

B. 9π

C. 16π

D. 25π

E. 36π

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A. 4π

B. 9π

C. 16π

D. 25π

E. 36π

callmeDP · Accepted Answer

The simplest approach by using the distance formula, which is given below:

Distance between two points is given by ( x1, y1 ) and ( x2,y2 )

D =  \sqrt{ (x1-x2)^2 + (y1-y2)^2 }

Now, here we will calculate the distance between (-8,-11) and (-8,-8). By using the above equation you will get D = 3 unit, Thus radius is more than 3

Now, here we will calculate the distance between (-8,-11) and (-11,-7). By using the above equation you will get D = 5 unit. Thus radius is less than 5

It is given that radius is an integer number. And to only number possible between 3 and 5 which is an integer is 4.

Hence, the radius is 4 units, and the Area of the circle is C.

Bryan180599 · Answer

In the xy-plane, the center of a circle is located at (−8, −11). The point (−8, −8) lies inside the circle, and the point (−11, −7) lies outside the circle. If the circle’s radius is an integer, what is its area?

A. 4π

B. 9π

C. 16π

D. 25π

E. 36π

Project PS Butler

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Let's say that point x is on the circle ==> Distance between point x and the center is the radius. We have to find x (integer).

We know that (-8,-8) is inside the circle so the distance between this point and the center is : -8-(-11) = 3 ==> we can deduce that x>3 (eliminate answer A and B)

Then we know that the point -11,-7. The distance is the hypotenuse of a triangle having the point (-8, -11) the center, (-11, -7) the point we have and another point (-8,-7). The distance between this new point are 3 and 4. So the hypotenuse is : x²=4²+3² = 16+9 = 25. Thus the distance between (-11,-7) and (-8, -11) is 5. As this point is outside the circle, x<5

Hence the radius should be greater than 3 but lower than 5. So Radius equal 4. Area = 4²*Pi = 16Pi

Answer C

For this question, I draw a little croquis on my sheet of paper. It helped me to find the value without doing calculations as you can directly deduce the distance between the center and the 2 points given in the question.

akadiyan · Answer

In the xy-plane, the center of a circle is located at (−8, −11). The point (−8, −8) lies inside the circle, and the point (−11, −7) lies outside the circle. If the circle’s radius is an integer, what is its area?

A. 4π

B. 9π

C. 16π

D. 25π

E. 36π

Project PS Butler

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Point inside the circle :
The point (-8 , -8) lies within the circle. 
We know the distance between the point inside the circle and the center of the circle is 3

So minimum radius of the circle is 3

Point outside the circle :
The point (-11 , -7) lies outside the circle. 
The distance between the point (-11 , -7) and the center of the circle is 5

So maximum value of radius of the circle is less than 5

Since the radius is integer and 3>r<5 , we have radius = 4

Area =  \pi r^2  =  \pi 4^2  =  16 \pi

Ans:  C

MHIKER · Answer

Distance from the center (-8,-11) to the inside point (−8, −8)  = D_1=\sqrt{(-8+8)^2+(-11+8)^2}

D_1=3

Distance from the center (-8,-11) to the outside point (−11, −7)  =D_2=\sqrt{(-8+11)^2+(-11+7)^2}

D_2= \sqrt{9+16}

D_2=5

So, the radius will be  3<r<5  and must be an integer. The integer between  3  and  5  is  4

Radius  (r) =4

Thus the are of the circle is  = \pi r^2=\pi 4^2 = 16 \pi

The answer is  C

exc4libur · Answer

centr = -8-11
insid = -8-8
outsid = -11-8

dis^2   = (-8--8)^2 + (-11--8)^2 = V(9) = 3
thus, r>3

dis^2   = (-8--11)^2 + (-11--8)^2 = V(9+9) = V(18)
thus, r<5

r=4
(C)

Solenja · Answer

i can understand what the question was asking but i feel like the question a little incomplete dont you think?(or may be its just me )

AsmaM · Answer

Is this on GMAT Focus?

Bunuel · Answer

_________________
No. Too geometry heavy.

In the xy-plane, the center of a circle is located at (8, 11). The

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In the xy-plane, the center of a circle is located at (8, 11). The

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