MathDB

SMT 2022 Geometry Tiebreaker #2

Source:

April 1, 2023

Problem Statement

The incircle of

\triangle ABC

is centered at

I

and is tangent to

BC

,

CA

, and

AB

at

D

,

E

, and

F

, respectively. A circle with radius

2

is centered at each of

D

,

E

, and

F

. Circle

D

intersects circle

I

at points

D_1

and

D_2

. The points

E_1

,

E_2

,

F_1

, and

F_2

are defined similarly. If the inradius of

\triangle ABC

is

5

, what is the ratio of the area of the triangle whose sides are formed by extending

D_1D_2

,

E_1E_2

, and

F_1F_2

to the area of

\triangle ABC

?

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