See complete Problem 115

Area of Triangles, Excircles. Level: High School, SAT Prep, College

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## Sunday, June 8, 2008

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Elearn Geometry Problem 115

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

See complete Problem 115

Area of Triangles, Excircles. Level: High School, SAT Prep, College

Post your solutions or ideas in the comments.

Subscribe to:
Post Comments (Atom)

S=r_A(p-a)=r_B(p-b)=r_C(p-c)

ReplyDeleteS1=S2=0.5r_C(p-c)

S3=S4=0.5r_A(p-a)

S5=S6=0.5r_B(p-b)

.-.

AM = BF = s-c

ReplyDeleteS1=1/2.rc.AM =1/2.rc.(s-c)=1/2.([ABC]/(s-c)).(s-c)

= 1/2.[ABC]

S2=1/2.rc.BF =1/2.rc.(s-c)=1/2.([ABC]/(s-c)).(s-c)

= 1/2.[ABC]

Then S1=S2

CH = BE = s-a

S3=1/2.ra.CH =1/2.ra.(s-a)=1/2.([ABC]/(s-a)).(s-a)

= 1/2.[ABC]

S4=1/2.ra.BE =1/2.ra.(s-a)=1/2.([ABC]/(s-a)).(s-a)

= c

Then S1=S2=S3=S4

with the way , it can be proved that :

S5=S6=1/2.[ABC] so

S1=S2=S3=S4=S5=S6=1/2.[ABC]