I got it!Thank you Takaki!
Takaki wrote:
> Hi zx.mys!
>
> This is my interpretation of the contest analysis solution:
>
> Originally, you have 3 circles of radii r1, r2 and r3 (say r1 is the
> smallest). The solution says to subtract the radii of the two larger circles
> to r2 - r1 and r3 - r1. These circles will be outside the smallest circle,
> so after inversion, they will be contained within the smallest circle. The
> tangents mean the straight lines that touch the two inverted circles (they
> won't necessarily go through the smallest circle's centre). Like this:
>
> ____O_o___
>
> When inverted back, the tangents will map to circles which touch the r2-r1
> and r3-r1 circles (because tangency is preserved by inversion) and goes
> through the centre of the smallest circle (lines map to circles that pass
> through origin), so the radius can be increased by r1 to get a circle which
> touches all three plants.
>
> I hope this helps! If you're not too familiar with inversion, I think
> wikipedia explains it quite well:
> http://en.wikipedia.org/wiki/Inversive_geometry
>
>
>
> On Mon, Sep 28, 2009 at 3:00 PM, Zx.MYS <[email protected]> wrote:
>
> >
> > quoted from Contest Analysis
> >
> > "We can subtract from the radius of each of the three plants the
> > radius of the smallest plant, then compute an inversion about that
> > plant's center. Then we find appropriate tangents to the two inverted
> > plants, re-invert to find the corresponding circle, and add back the
> > radius of the smallest plant. "
> >
> > I got puzzled when trying to understand this(may caused by my poor
> > English).
> > Why doing all these inversions? Doe "appropriate tangents" mean a
> > tangents go through the smallest plant's center?
> > And finally,how does this solution work?
> >
> > >
> >
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