MathDB

11

Part of 2018 Baltic Way

Problems(1)

A funny twist of geometry with number theory

Source: Baltic Way 2018, Problem 11

11/6/2018
The points A,B,C,DA,B,C,D lie, in this order, on a circle ω\omega, where ADAD is a diameter of ω\omega. Furthermore, AB=BC=aAB=BC=a and CD=cCD=c for some relatively prime integers aa and cc. Show that if the diameter dd of ω\omega is also an integer, then either dd or 2d2d is a perfect square.
geometrynumber theory