See complete Problem 116

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

Post your solutions or ideas in the comments.

## Sunday, June 8, 2008

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## Sunday, June 8, 2008

###
Elearn Geometry Problem 116

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

See complete Problem 116

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

Post your solutions or ideas in the comments.

Subscribe to:
Post Comments (Atom)

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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