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hi everyone! I hope y'all are doing well during this tough period of time.  I really need help on this and would appreciate it if someone helped me. Thanks!

 

A circle centered at A with radius 10 is externally tangent to a circle centered at B with radius 7.  A line that is externally tangent to both circles is drawn, where both circles lie on the same side of the line. This line intersects line AB at C. Find the length BC.

 

Thank you!

 Apr 17, 2020
 #1
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A circle centered at A with radius 10 is externally tangent to a circle centered at B with radius 7.  A line that is externally tangent to both circles is drawn, where both circles lie on the same side of the line. This line intersects line AB at C. Find the length BC.

laugh

 Apr 17, 2020
 #2
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Let X be the point where the external tangent meets circle A.

Let Y be the point where the external tangent meets circle B.

 

Because AX is perpendicular to CYX and BY is perpendicular to CYX, triangle(ACX) is similar to triangle(BCY).

 

Therefore:  CB : CA  =  BY : AX.

Since  CA  =  CB + BA  =  CB + 17  and  BY  =  7  and  AX  =  10:

--->   CB : CB + 17  =  7 : 10

--->  10 · CB  =  7 · (CB + 17)

 

Can you finish it from here?

 Apr 17, 2020
 #3
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Thank you both so much, it helped a lot!  Hope you have a great day! :)

 Apr 17, 2020

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