MathDB

Rational Coordinates

Source: 1992 IrMO Paper 1 Problem 5

October 2, 2017

geometryanalytic geometry

Problem Statement

Let

ABC

be a triangle such that the coordinates of the points

A

and

B

are rational numbers. Prove that the coordinates of

C

are rational if, and only if,

\tan A

\tan B

, and

\tan C

, when defined, are all rational numbers.