MathDB

Let

C

be a variable interior point of a fixed segment

AB

. Equilateral triangles

ACB'

and

CBA'

are constructed on the same side and

ABC'

on the other side of the line

AB

. (a) Prove that the lines

AA' ,BB'

, and

CC'

meet at some point

P

. (b) Find the locus of

P

C

varies. (c) Prove that the centers

A'' ,B'' ,C''

of the three triangles form an equilateral triangle. (d) Prove that

A'' ,B'',C''

, and

P

lie on a circle.

Problem Statement