MathDB

there exists a unique point P equidistant from A and B'

Source: Vietnam TST 1994 for the 35th IMO, problem 4

June 25, 2005

geometrycircumcirclegeometric transformationrotationsymmetrygeometry solved

Problem Statement

Given an equilateral triangle

M

and a point

M

in the plane (

ABC

). Let

A', B', C'

be respectively the symmetric through

M

of

A, B, C

. I. Prove that there exists a unique point

P

equidistant from

D

and

AB

, from

B

and

C'

and from

C

and

A'

. II. Let

AP

be the midpoint of the side

AB

. When

M

varies (

M

does not coincide with

D

), prove that the circumcircle of triangle

MNP

(

N

is the intersection of the line

DM

and

AP

) pass through a fixed point.

Back to Problems View on AoPS