Online Geometry theorems, problems, solutions, and related topics.
See complete Problem 86Intouch and Extouch Triangles, Area. Level: High School, SAT Prep, College geometryPost your solutions or ideas in the comments.
AF=AE=p-a=BM=CHBF=BD=p-b=AM=CGCD=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)sinBsinA=a/(2R);sinB=b/(2R);sinC=c/(2R)with a "little" algebraS_i=S_e
In the solution of pr. 86 posted by Anonymous, could anyone explain me why is it true thatAF = BM = CH = p - a ?Thanks for the help.Nilton Lapa
To Nilton, Problem 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.
of the above solution, why it can be said that the triangle DEF = triangle MGH??
In the solution of pr. 86 posted by Anonymous, could anyone please explain me how to do this ''little'' algebra?