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1. 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 intersects line AB at C. Find the length BC.

3. Mar 13, 2020

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2. Help! Mar 13, 2020
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1. By similar triangles, BC = 13*10/7 = 130/7.

3. By similar triangles, YZ = 14^2/8 = 49/2.

Mar 13, 2020
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1)  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 intersects line AB at C. Find the length BC.

BC = 39.66666672 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2)           AB = 2        x = 1       CD = 4.5     y = 2.25

r = sqrt ( xy ) = sqrt ( 1 * 2.25 ) = 1.5 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

3)           XY = 14            WX = 8

tan(Y) = 8 / 14        ∠Y = 29.7448813°

XZ = tan(Y) * WX = 4.571428571

YZ = XY - XZ = 9.428571429

YZ ≈ 9.428 Mar 13, 2020
edited by Guest  Mar 13, 2020
edited by Dragan  Mar 13, 2020
edited by Dragan  Mar 13, 2020
edited by Dragan  Mar 20, 2020
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Question 3

The guest here    https://web2.0calc.com/questions/help-asap_85440

Says that Dragan's answer is incorrect.

So I graphed it to scale.

I got the same answer as Dragan.  (they are both approximate)

*Although Dragan has not used universal logic.

He has looked at the specific case where WY is a diameter of the circle.

And then he has assumed that it will be the same in all other cases as well.

https://www.geogebra.org/classic/avx3arkb  Oct 10, 2020
edited by Melody  Oct 10, 2020