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Two circles have the same center O. Point X is the midpoint of segment OP. What is the ratio of the area of the circle with radius OX to the area of the circle with radius OP? Express your answer as a common fraction.
 

I got so confused so I drew a pic....

IDK what to do from there...

 Aug 30, 2019
 #1
avatar+23884 
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Two circles have the same center O.

Point X is the midpoint of segment OP.

What is the ratio of the area of the circle with radius OX to the area of the circle with radius OP?

 

\(\begin{array}{|rcll|} \hline A_1 &=& \pi \times OX^2 \\ A_2 &=& \pi \times OP^2 \\ \hline \dfrac{A_1}{A_2} &=& \dfrac{\pi\times OX^2} {\pi\times OP^2} \\\\ \dfrac{A_1}{A_2} &=& \dfrac{ OX^2} { OP^2} \quad | \quad OP = 2\times OX \\\\ \dfrac{A_1}{A_2} &=& \dfrac{ OX^2} { \left(2\times OX \right)^2} \\\\ \dfrac{A_1}{A_2} &=& \dfrac{ OX^2} { 4\times OX^2} \\\\ \mathbf{\dfrac{A_1}{A_2}} &=& \mathbf{ \dfrac{1} { 4 } } \quad \text{ or } \quad \mathbf{\dfrac{A_1}{A_2}} = \mathbf{ \left(\dfrac{1}{2}\right)^2 }\\ \hline \end{array}\)

 

laugh

 Aug 30, 2019
edited by heureka  Aug 30, 2019
 #2
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Thank you- can you just do (1/2)^2?

tommarvoloriddle  Aug 30, 2019

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