See complete Problem 115
Area of Triangles, Excircles. Level: High School, SAT Prep, College
Post your solutions or ideas in the comments.
Sunday, June 8, 2008
Elearn Geometry Problem 115
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See complete Problem 115
Area of Triangles, Excircles. Level: High School, SAT Prep, College
Post your solutions or ideas in the comments.
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]