See complete Problem 116
Area of Triangles, Excircles, Tangent. Level: High School, SAT Prep, College geometry
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Sunday, June 8, 2008
Elearn Geometry Problem 116
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S1+S2+[BGFH]=[PBE]
ReplyDeleteS3+S4+[BGFH]=[DBQ]
[PBE]=0.5BP.BE.sin(PBE)
[DBQ]=0.5DB.BQ.sin(DBQ)
line PBQ is the exterior bisector of ang(ABC)
ang(PBE)=(180-B)/2+ang(DBE)=ang(DBQ)
The right triangles PBD and BQE are similar
BP.BE=DB.BQ
hence [PBE]=[DBQ] and S1+S2=S3+S4
.-.
BE = (s-c)
ReplyDelete[BPE]=1/2.rc.(s-c)=1/2.([ABC]/(s-c).(s-c)
=1/2.([ABC]
BD = (s-a)
[BDQ]=1/2.ra.(s-a)=1/2.([ABC]/(s-a).(s-a)
=1/2.([ABC]
So [BPE] =[BDQ]
[BPE]-[BGFH]=[BDQ]-[BGFH]
S1+S2 = S3+S4
widarto teddy
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