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.

## Saturday, April 16, 2016

### Geometry Problem 1208: Triangle, Circle, Excircle, Excenter, Diameter, Perpendicular, Equal Areas

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http://s22.postimg.org/8bjm3kpox/pro_1208.png

ReplyDeleteDraw 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/AF

In this transformation, tri. AB’C’ become tri ABC , circle E become incircle I of tri. ABC, F become G

So 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?

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