MathDB

a line passing through the incenter

Source: bmo 1986

April 23, 2007

geometryincentercircumcirclegeometry proposed

Problem Statement

A line passing through the incenter

I

of the triangle

ABC

intersect its incircle at

D

and

E

and its circumcircle at

F

and

G

, in such a way that the point

D

lies between

I

and

F

. Prove that:

DF \cdot EG \geq r^{2}

.

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