MathDB

concyclic wanted, <MBA=<LBC, BK=BC, BF=AB, circles with diameters AB,AC

Source: 2003 Oral Moscow Geometry Olympiad grade 9 p3

October 26, 2020

geometryequal segmentsequal anglesConcyclic

Problem Statement

Inside the segment

AC

, an arbitrary point

B

is selected and circles with diameters

AB

and

BC

are constructed. Points

M

and

L

are chosen on the circles (in one half-plane with respect to

AC

), respectively, so that

\angle MBA = \angle LBC

. Points

K

and

F

are marked, respectively, on rays

BM

and

BL

so that

BK = BC

and

BF = AB

. Prove that points

M, K, F

and

L

lie on the same circle.