common tangents

king_of_inismac

ok, looks like a simple question, but its kinda tricky.


Two circles, C1 and C2 which overlap.

I know their centre points and their radii (ones bigger than the other), so I know their equations.

I need to find the equations of their common tangents?

Does anyone have any ideas?

I'm not going to post my attempts yet, as I don't want to influence how anyone approaches it.

Thanks!

Squirrel

Can you give us the centre points and radii?

Yakuza

This doesn't answer your question, but here's a nice applet to illustrate common tangents:

http://www.ies.co.jp/math/products/geo2/applets/comtan/comtan.html

As can be seen with the applet, there are several cases to consider:

1) d > a+b (4 common tangents)
2) d = a+b (3)
3) d < a+b (2)
4) d = a-b (1)
5) d < a-b (none)

Kenshi

This is one I might get this year in the Leaving in June.

Take the equation of one cirlce away from the other.

ie. Tangent between circles S1: x^2+y^2+ax+by+c and x^2+y^2+mx+ny+d
=
(x)^2+(y)^2+ax+by+c-[(x)^2+(y)^2+mx+ny+d]

(This solution only works as the circles overlap)