MathDB

Circumcenter and orhocenter

Source: Bosnia and Herzegovina TST 2014 day 2 problem 3

May 11, 2014

geometrycircumcircleangle bisectorperpendicular bisectorgeometry unsolved

Problem Statement

Let

D

and

E

be foots of altitudes from

A

and

B

of triangle

ABC

F

be intersection point of angle bisector from

C

with side

AB

, and

O

I

and

H

be circumcenter, center of inscribed circle and orthocenter of triangle

ABC

, respectively. If

\frac{CF}{AD}+ \frac{CF}{BE}=2

, prove that

OI = IH