Ali Devin sezer (e106184++at++metu.edu.tr)
Mon, 3 Jan 2000 20:04:35 +0200 (WET)
Two circles are tangent to each other means that they
have a common tangent line at one point.
I assume that the two circles lie on the same plane:
Let P be the point where these circles touch each other.
let T be their common tangent. let O1 be the center of the first
one. let O2 be the center of the second one. the line ( call it
L1 ) that contains both O1 and P and the line ( call it L2)
that contains both O2 and P are both perpendicular
to T ( because they are the normals of the first and second
circles respectively - a trivial fact from analytic geometry
, and normal is by definition perpendicular to the tangent).
Hence L1 and L2 are paralel ( because we are in
a plane ). moreoever they intersect at P. Hence they are one and
the same line which contains all O1, O2 and P.
Q.E.D.
On Sat, 1 Jan 1994, Jane Moore wrote:
> I would be very happy if you could help me solve this problem:
>
> Prove that the point of contact of two tangent circles is on the line
> joining the centres of the two circles.
>
> Thanks,
> Jane
>
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