Online Geometry theorems, problems, solutions, and related topics.
Geometry Problem. Post your solution in the comment box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the figure below to view more details of problem 1208.
http://s22.postimg.org/8bjm3kpox/pro_1208.pngDraw line B’FC’ //BC and tangent to circle E at F ( see sketch)Circle E become incircle of triangle AB’C’Perform homothetic transformation, center A and scaling factor= AB/AB’=AC/AC’=AG/AFIn this transformation, tri. AB’C’ become tri ABC , circle E become incircle I of tri. ABC, F become GSo G is the tangent point of incircle I of triangle ABC to BC So BG=DC=p – AC ( p= haft perimeter of triangle ABC)Triangles BGF and FDC have same base and altitude so these triangles have same area.
Do you have another proof for this Antonio?