Geometry Problem. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

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## Wednesday, April 1, 2015

### Problem 1105: Triangle, Incircle, Excircle, Cevian, Tangent, Congruence, Geometric Mean

Labels:
circle,
congruence,
excircle,
geometric mean,
incircle,
tangent,
triangle

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This is two Sangaku with equal incircles problem . See link below for solution in details.

ReplyDeletehttp://s25.postimg.org/ghxiz2xbz/two_sangaku_with_equal_incircles_problem.png

The length of cevian BD will be x= BD= sqrt(s.(s-b)) per above link.

In our case s= AF= ½ of perimeter of triangle ABC

s-b= AF-AC= CF

so BD=sqrt(AF.CF)