Wednesday, April 1, 2015

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

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Click the diagram below to enlarge it.

Online Math: Geometry Problem 1105: Triangle, Incircle, Excircle, Cevian, Tangent, Congruence, Geometric Mean.

Posted by Antonio Gutierrez at 4:02 PM
Labels: , , , , , ,

1 comment:

  1. Peter TranApril 2, 2015 at 4:40 PM

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

    ReplyDelete

Subscribe to: Post Comments (Atom)