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In isosceles right triangle ABC, shown here, AC = BC. Point X is on side BC such that CX  = 6 and XB = 12, and Y is on side AB such that XY is perpendicular to AB. What is the ratio of BY to YA?

 

 Feb 12, 2021
 #1
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Note  that  since  BC  = AC, then   BA =  18sqrt (2)

 

Note  that triangle  YBX  is similar  to  triangle CBA 

 

Therefore

 

BY  / BX  =  CB  / BA

 

BY  / 12 =  18 / (18 sqrt (2)

 

BY /12  =  1/sqrt 2

 

BY      =  12/  sqrt (2)   =   6 sqrt (2)

 

So   YA =   BA - BY =   18sqrt 2 -  6 sqrt 2  =  12 sqrt 2

 

So

 

BY  :  YA  =   6sqrt (2)   :  12 sqrt (2)  =    1 :  2

 

 

cool cool cool

 Feb 12, 2021

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