MathDB

Given a rhombus

ABCD

. A point

M

is chosen on its side

BC

. The lines, which pass through

M

and are perpendicular to

BD

and

AC

, meet line

AD

in points

P

and

Q

respectively. Suppose that the lines

PB,QC,AM

have a common point. Find all possible values of a ratio

\frac{BM}{MC}

. S. Berlov, F. Petrov, A. Akopyan

Problem Statement