MathDB

On side

AB

of triangle

ABC

, points

M

and

K

are taken (

M

on segment

AK

). It is known that

AM: MK: MB = a: b: c

. Straight lines

CM

and

CK

intersect for the second time the circumscribed circle of the triangle

ABC

at points

E

and

F

, respectively. In what ratio does the circumscribed circle of the triangle

BMF

divide the segment

BE

Problem Statement