MathDB

Interior bisectors of the angles A,B and C

Source: IMO ShortList 1988, Problem 3, Canada 1, Problem 4 of ILL

October 22, 2005

geometrycircumcircletrigonometryinradiusgeometric inequalityIMO Shortlist

Problem Statement

The triangle

ABC

is inscribed in a circle. The interior bisectors of the angles

A,B

and

C

meet the circle again at

A', B'

and

C'

respectively. Prove that the area of triangle

A'B'C'

is greater than or equal to the area of triangle

ABC.