Trignometry IS What You Answer
Geometry
Level
3
a,b and c are the sides of triangle.
R is the circumradius, r is the inradius, s is the semiperimeter.
What is
1/ab + 1/bc + 1/ca = ?
1/2R + s/2r
1/2rs
1/2Rr
s/2R
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1 solution
The area of triangle ABC = ab/2 = (a+b+c) r/2, so r=ab/( a+b+c).where c=2R. 1/ab + 1/bc + 1/ca = (c+b+a)/abc = 1/(2rR)