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

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

Click the figure below to view the complete problem 991

## Saturday, March 8, 2014

### Geometry Problem 991: Triangle, Incircle, Tangent Points, Isosceles, Midpoint, Collinearity, Congruence, Circle

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Let altitude BK of triangle ABC cut EF at N and AC at K

ReplyDeletelet incircle I tangent to AC at L

Let p and p’ are haft perimeter of triangles BDC and ABC

Using properties of incircles I , I1 and isosceles triangle ABD we have LE= p’-p => LE=AK=KD

We also have ∠(DEF)=1/2∠(FDA)= ∠(IAL) and AL=KE

Triangles ALI congruent to EKN => KLIN is a rectangle

Since DE=KL=NI => DEIN is a parallelogram and diagonals will bisect each other.