In the diagram above, point B is the center of Circle #1 and point D i

Question

gpp_img7.png In the diagram above, point B is the center of Circle #1 and point D is the center of Circle #2. If the ratio of the area of Circle #2 to the area of Circle #1 is 3:2, what is the ratio CE:BC? A. 1.5 B. \sqrt{3} C. 3 D. \sqrt{6} E. 6 Kudos for a correct solution .

iamdp · Answer

Hi

let's say R1 is the radius of smaller circle and R2 is of the bigger circle

According to question 
A1/A2 = 3/2
  /   = 3/2
R1/R2 = root3 / root 2

Now CE= 2  & BC =R1

therefore CE/BC =   / root2 = root6

lipsi18 · Answer

Assume radius of circle 1 = R & radius of circle 2 = r; 
given, Area of Circle 1/Area of Circle 2 = 3/2 = R^2/r^2; therefore R/r = Root 3/Root 2
Required, CE:BC = 2*R: r = 2 * Root 3/Root 2; simplify (multiply numerator and denominator by root 2), and answer = Root 6
Therefore answer choice D Root 6

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

This is tricky. We are given the ratio of areas, and we want to know a ratio involving the radii. Let R be the radius of the bigger circle, and r be the radius of the smaller circle.
 ratio \ of \ areas = \frac{3}{2} = \frac{\pi{R^2}}{\pi{r^2}}=\frac{\pi{R^2}}{\pi{r^2}} .

Take the  square root and rationalize the denominator :
 \frac{R}{r}=\frac{\sqrt{3}}{\sqrt{2}}=\frac{\sqrt{6}}{2}

Well, CE = 2R, and BC = r, so CE/BC = 2R/r, which is twice this ratio  \frac{CE}{BC}=\sqrt{6} .

Answer = (D)

kashifgolf · Answer

gpp_img7.png In the diagram above, point B is the center of Circle #1 and point D is the center of Circle #2. If the ratio of the area of Circle #2 to the area of Circle #1 is 3:2, what is the ratio CE:BC? A. 1.5 B. \sqrt{3} C. 3 D. \sqrt{6} E. 6 Solution : Lets assume radius of circle 1 - r, and circle 2 as - R Area of circle 1 - pi r*2 Area of circle 2 - pi R*2 Therfore pi R*2/pi r*2 = 3/2 R*2/r*2 = 3/2 R/r = root 3/ root 2 We have to find out the ratio of the diameter of circle 2/ radius of circle 1, which can be written mathematically as 2R/r 2R/r = 2* root 3/ root 2 = root 2 * root 3 = root 6 Answer : D

shashankism · Answer

Area(C2) : Area (C1) = 3 :2 
Diameter(C2) : Diameter(C1) =  \sqrt{(3/2)}  
CE: AB =  \sqrt{(3/2)}  
CE: 2BC =  \sqrt{(3/2)}  
CE:BC = 2* \sqrt{(3/2)}  =  \sqrt{4*(3/2)}  =  \sqrt{6}

Answer D

bumpbot · Answer

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In the diagram above, point B is the center of Circle #1 and point D i

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