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In square ABCD, AD is 4 centimeters, and M is the midpoint of CD. Let O be the intersection of AC and BM. What is the ratio of OC to OA? Express your answer as a common fraction.

 

 Nov 4, 2018
 #1
avatar+102948 
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Angle AOB   = Angle MOC

And angle CMB  = angle ABM

 

So...by AA congruency....

 

Triangle BOA  is similar to triangle  MOC

 

And since  AB  =  AD = 4   and MC  = 2 .....then  the scale factor of triangle MOC to triangle BOA is 2 : 4  =    1 : 2

 

So

 

OC : OA   =   1 : 2   =   1 / 2 

 

 

 

cool cool cool

 Nov 4, 2018
edited by CPhill  Nov 4, 2018

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