MathDB

Given two directly congruent triangles

ABC

and

A'B'C'

in a plane, assume that the circles with centers

C

and

C'

and radii

CA

and

C'A'

intersect. Denote by

\mathcal M

the transformation that maps

\triangle ABC

\triangle A'B'C'

. Prove that

\mathcal M

can be expressed as a composition of at most three rotations in the following way: The first rotation has the center in one of

A,B,C

and maps

\triangle ABC

\triangle A_1B_1C_1

; The second rotation has the center in one of

A_1,B_1,C_1

, and maps

\triangle A_1B_1C_1

\triangle A_2B_2C_2

; The third rotation has the center in one of

A_2,B_2,C_2

and maps

\triangle A_2B_2C_2

\triangle A'B'C'

Problem Statement