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https://web2.0calc.com/questions/tangents-on-a-circle-please-explain

 Jun 9, 2020
 #1
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There are two externally tangent circles, circle(A) with radius = 10 and circle(B) with radius = 7.

Therefore, AB = 17.

 

There is an externally tangent line (with both circle(A) and circle(B) on the same side of the line)

XY, where X is the point of intersection with circle(A) and Y is the point of intersection with circle(B).

Therefore, AX = 10 and BY = 7.

 

Extend both AB and XY so they intersect at point C.

 

Triangle(ACX) will be similar to triangle(BCY) because they have corresponding congruent angles.

Call BC = x.  This makes AC = x + 17.

 

This means that:  AX / BY  =  AC / BC.   --->   10 / 7  =  (x + 17) / x

--->   10x  =  7(x + 17)   --->   10x  =  7x + 119   --->   3x  =  119   --->   x  =  119/3

 

BC  =  119/3

 Jun 9, 2020

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