🚀 go-pugleaf

 The circle asked for is of course known as the in-circle of the
triangle. I won't spoil people's fun in solving it, but the answer is 
one of those cases where you will say "gee that's neat -- I didn't
know that!"
As an extension:  draw the 3-4-5 triangle and label as ABC (B at the 90
degree angle). Extend all three sides. Now find the radii of the
three circles, each of which is tangent to one of the sides (extrnally)
and the other two sides extended. For instance, one such circle
is tangent to BC and to AC extended and to AB extended. Again, 
the results are not well-known and are "interesting".

On a related note:  Students learn in high school trig about the
law of Sines (at least I HOPE they still do!!! :-) ) which says
that the ratio a/sin A = b?sin B = c/sin C. That is, this
particular ratio is a constant. The question for you out there in
math=-land is: what is the significance of this particular
constant? i.e., what does it have to do with the original
triangle. Another gee whiz type answer.
enjoy
mike
bolduan @catlin    onn bitnet
bolduan@catseq.catlin.edu    on internet
-- 
mike bolduan
bolduan@catlin