MathDB

Let the triangle

ABC

have area

1

. The interior bisectors of the angles

\angle BAC,\angle ABC, \angle BCA

intersect the sides

(BC), (AC), (AB)

and the circumscribed circle of the respective triangle

ABC

at the points

L

and

G, N

and

F, Q

and

E

. The lines

EF, FG,GE

intersect the bisectors

(AL), (CQ) ,(BN)

respectively at points

P, M, R

. Determine the area of the hexagon

LMNPR

7