geometry

 

In the diagram, a = 4 and b = 9.  Find x.     

 

Draw a line from center of small circle perpendicular to radius of large circle.     

 

That new line, call it Z, is parallel to x, which makes it the same length as x.     

 

Z is also a side of a right triangle with 1 side = (9 – 4) and the hypotenuse = (9 + 4).     

 

So Z  =  sqrt(13² – 5²)  =  sqrt(144)     

 

Z = x     ——>>          x  =  12     

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