Thursday, July 24, 2008

Elearn Geometry Problem 142

Four triangles, incircle, areas

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.

3 comments:

  1. triangles AMH,BDE,CFG are similar to ABC.
    sqr(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)

    ReplyDelete
    Replies
    1. note that D,O, G are colinear .M,O,F and H,O,E are conlinear.
      we also have DO=OG, MO=OF and OE=OH
      so triangle MOD congruent to FOG ( case SAS) and MD= FG

      Peter Tran

      Delete