MathDB

A'B' > diameter of incircle, <A'C'B'=90^o

Source: 2006 Oral Moscow Geometry Olympiad grades 8-9 p3

October 17, 2020

geometrygeometric inequalityinradiusright angle

Problem Statement

On the sides

AB, BC

and

AC

of the triangle

ABC

, points

C', A'

and

B'

are selected, respectively, so that the angle

A'C'B'

is right. Prove that the segment

A'B'

is longer than the diameter of the inscribed circle of the triangle

ABC

.
(M. Volchkevich)