SOLUTION: The circumcenter of triangle ABC is S. AS extended intersect BC at M. BS extended intersect AC at N. CS extended intersect AB at P. If the circumradius is R, what is {{{ 1/AM + 1/B

Question 1062345: The circumcenter of triangle ABC is S. AS extended intersect BC at M. BS extended intersect AC at N. CS extended intersect AB at P. If the circumradius is R, what is ?
Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
AM, BN, CP are perpendicular bisectors since all three intersect at S
:
AM = R + r, where R is the circumradius and r in the inner radius
:
(1/AM) + (1/BN) + (1/CP) = ( (3/R+r) )
:

Answer by ikleyn(52874) (Show Source): You can put this solution on YOUR website!
.
"The circumcenter is the center of a triangle's circumcircle. It can be found as the intersection of the perpendicular bisectors."

From http://mathworld.wolfram.com/Circumcenter.html

The proof by "rothauserc" seems to be strange and incorrect, starting from the first line.

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