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

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

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## Wednesday, October 14, 2015

### Geometry Problem 1153: Triangle, Angle Bisectors, Perpendicular, Congruence

Labels:
angle bisector,
congruence,
perpendicular,
triangle

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Let I is incenter of triangle ABC

ReplyDeleteLet BI meet AC at L

Observe that EBDI is a complete quadrangle so L, F are harmonic conjugate points of A and C.

Since BL is an internal bisector of angle ABC So BL is external bisectors of angle ABC and FH=FG

this problem need

ReplyDelete1) BF bisector of CBH

2) IBF = 90

3) BI // GH

4) GB = BH

It is possible in another construcsion included AB > BC