MathDB

Let

ABC

be a non-equilateral triangle in the plane, and let

T

be a point different from its vertices. Define

A_T

B_T

and

C_T

as the points where lines

AT

BT

, and

CT

meet the circumcircle of

ABC

. Prove that there are exactly two points

P

and

Q

in the plane for which the triangles

A_PB_PC_P

and

A_QB_QC_Q

are equilateral. Prove furthermore that line

PQ

contains the circumcenter of

\triangle ABC

Problem Statement