Challenging Geometry Puzzle: Problem 1590. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.
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Using standard triangle notation
ReplyDeleteS(OEH) = (r/2).(c/2 - (s-a)) = 10............(1)
S(ODG) = (r/2).((s-c) - b/2) = 24............(2)
S(OFM) = (r/2).(a/2 - (s-b)) ...................(3)
(2) - (1); 14 = (r/2).(b - c)/2 upon simplification and
(3); S(OFM) = (r/2).(b - c)/2 upon simplification
It follows that S(OFM) = 14 since the RHS are the same
Sumith Peiris
Moratuwa
Sri Lanka
assume that a>b>c
ReplyDeletewe have DG= AG-AD= b/2-(p-a)=(a-c)/2
simillarly FM= BM-BF=(b-c)/2
and HE=BE-BH=(a-b)/2
note that DG=FM+HE
so S(OFM)=S(ODG)-S(OEH)= 14