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