MathDB

Given is a triangle

ABC

with side lengths

a, b, c

(

a = \overline{BC}

b = \overline{CA}

c = \overline{AB}

) and area

F

. The side

AB

is extended beyond

A

by a and beyond

B

b

. Correspondingly,

BC

is extended beyond

B

and

C

b

and

c

, respectively. Eventually

CA

is extended beyond

C

and

A

c

and

a

, respectively. Connecting the outer endpoints of the extensions , a hexagon if formed with area

G

. Prove that

\frac{G}{F}>13

Problem Statement