(In reply to
Solution by K Sengupta)
In going from
BE + EC < BZ + ZY + YC = (1/2)*(AB + BC + AC)
to
Or, 2R < R*(sin A + sin B + sin C) (in terms of the law of sines)
it would seem that a substitution has been made of R*sinA for (1/2)*AB, etc. It is not the case that they are equal, but apparently the inference is valid as R*sinA is bigger than (1/2)*AB, etc. I don't see, though what application of the law of sines you are using.
Could you make the application of the law of sines explicit, in terms of side1/sin(angle1) = side2/sin(angle2), and, in light of the inequality, rather than equality in the substitution, demonstrate that a larger term has been substituted for a smaller rather than the other way around?
Geometer's Sketchpad confirms that the substituted terms are indeed bigger, but I'd like to see how this is proved.
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Posted by Charlie
on 2007-10-14 10:37:43 |
re: Solution
