MathDB

An isosceles triangle

ABC

with AB \equal{} AC is given on the plane. A variable circle

(O)

with center

O

on the line

BC

passes through

A

and does not touch either of the lines

AB

and

AC

. Let

M

and

N

be the second points of intersection of

(O)

with lines

AB

and

AC

, respectively. Find the locus of the orthocenter of triangle

AMN

Problem Statement