See complete Problem 142

Four Triangles, Incircle, Tangent and Parallel to Side, Areas. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

## Thursday, July 24, 2008

### Elearn Geometry Problem 142

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triangles AMH,BDE,CFG are similar to ABC.

ReplyDeletesqr(S1/S)+sqr(S2/S)+sqr(S3/S)=AM/AB+DB/AB+GF/AB

but GF=MD and AM+MD+DB=AB

AB/AB=1

then sqr(S1)+sqr(S2)+sqr(S3)=sqr(S)

How GF=MD

Deletenote that D,O, G are colinear .M,O,F and H,O,E are conlinear.

Deletewe also have DO=OG, MO=OF and OE=OH

so triangle MOD congruent to FOG ( case SAS) and MD= FG

Peter Tran