See complete Problem 85

Contact Triangles Areas, Incircle, Excircle. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

## Monday, May 19, 2008

### Geometry Problem 85

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## Monday, May 19, 2008

###
Geometry Problem 85

Online Geometry theorems, problems, solutions, and related topics.

See complete Problem 85

Contact Triangles Areas, Incircle, Excircle. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

Subscribe to:
Post Comments (Atom)

S area of triangle ABC

ReplyDeleteS=pr=r_a(p-a)=r_b(p-b)=r_c(p-c)

1/r_a+1/r_b+1/r_c=(p-a+p-b+p-c)/S=p/(pr)=1/r

with the results of pb83 and pb84

1/S_a+1/S_b+1/S_c=2R/S(1/r_a+1/r_b+1/r_c)=

2R/(rS)=1/S_1

.-.

Here is a slightly different solution to problem 85.

ReplyDeleteAs the area of triangle ABC is S = pr = (p-a).ra = (p-b).rb = (p-c).rc, then 1/ra + 1/rb + 1/rc = (1/pr).(p-a+p-b+p-c)=(1/pr).(3p-2p)=1/r.

From the results of problem 84 we have S1/Sa + S1/Sb + S1/Sc = r(1/ra + 1/rb + 1/rc) = 1, so 1/Sa + 1/Sb + 1/ Sc = 1/S.