See complete Problem 86
Intouch and Extouch Triangles, Area. Level: High School, SAT Prep, College geometry
Post your solutions or ideas in the comments.
Monday, May 19, 2008
Geometry Problem 86
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See complete Problem 86
Intouch and Extouch Triangles, Area. Level: High School, SAT Prep, College geometry
Post your solutions or ideas in the comments.
AF=AE=p-a=BM=CH
ReplyDeleteBF=BD=p-b=AM=CG
CD=CE=p-c=BG=AH
[DEF]=[ABC]-0.5(p-a)²sinA-0.5(p-b)²sinB
-0.5(p-c)²sinC
[MGH]=[ABC]-0.5(p-b)(p-c)sinA-0.5(p-a)(p-b)sinC
-0.5(p-a)(p-c)sinB
sinA=a/(2R);sinB=b/(2R);sinC=c/(2R)
with a "little" algebra
S_i=S_e
In the solution of pr. 86 posted by Anonymous, could anyone explain me why is it true that
ReplyDeleteAF = BM = CH = p - a ?
Thanks for the help.
Nilton Lapa
To Nilton,
DeleteProblem 86, See
Semiperimeter s, Incircle and Excircles" or
Semiperimeter Index" or
use "two tangent segments to a circle from an external point are congruent."
To Antonio: thanks for the hints. My doubt is solved now.
ReplyDeleteof the above solution, why it can be said that the triangle DEF = triangle MGH??
ReplyDeleteIn the solution of pr. 86 posted by Anonymous, could anyone please explain me how to do this ''little'' algebra?
ReplyDelete