MathDB

Clocks with hand endpoint forming an equilateral triangle

Source: 1961 All-Russian Olympiad

August 4, 2015

geometryEquilateral TriangleRussia

Problem Statement

Points

A

and

B

move on circles centered at

O_A

and

O_B

such that

O_AA

and

O_BB

rotate at the same speed. Prove that vertex

C

of the equilateral triangle

ABC

moves along a certain circle at the same angular velocity. (The vertices of

ABC

are oriented clockwise.)