MathDB

locus of intersection of 2 circles

Source: II Soros Olympiad 1995-96 R1 9.9 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

June 2, 2024

geometryLocus

Problem Statement

Two points

A

and

B

are given on the plane. An arbitrary circle passes through

B

and intersects the straight line

AB

for second time at a point

K

, different from

A

. A circle passing through

A

K

and the center of the first circle intersects the first one for second time at point

M

. Find the locus of points

M