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...

tommarvoloriddle Aug 30, 2019

#1**+3 **

**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?**

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

heureka Aug 30, 2019