MathDB

Let

D,E,F

be the points of tangency of the incircle of a given triangle

ABC

with sides

BC, CA, AB,

respectively. Denote by

I

the incenter of

ABC

, by

M

the midpoint of

BC

and by

G

the foot of the perpendicular from

M

to line

EF

. Prove that the line

ID

is tangent to the circumcircle of the triangle

MGI

Problem Statement