MathDB

Problem 2

Part of 1974 Yugoslav Team Selection Test

Problems(1)

triangle, transformation as composition of three

Source: Yugoslav TST 1974 P2

5/29/2021
Given two directly congruent triangles ABCABC and A′B′C′A'B'C' in a plane, assume that the circles with centers CC and C′C' and radii CACA and C′A′C'A' intersect. Denote by M\mathcal M the transformation that maps △ABC\triangle ABC to △A′B′C′\triangle A'B'C'. Prove that M\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,CA,B,C and maps △ABC\triangle ABC to △A1B1C1\triangle A_1B_1C_1; The second rotation has the center in one of A1,B1,C1A_1,B_1,C_1, and maps △A1B1C1\triangle A_1B_1C_1 to △A2B2C2\triangle A_2B_2C_2; The third rotation has the center in one of A2,B2,C2A_2,B_2,C_2 and maps △A2B2C2\triangle A_2B_2C_2 to △A′B′C′\triangle A'B'C'.
geometrytransformationsTriangles