MathDB

Iran TST 2009-Day1-P1

Source:

May 9, 2009

geometryincenterinradiustrigonometrygeometry proposed

Problem Statement

Let

ABC

be a triangle and

A'

B'

and

C'

lie on

BC

CA

and

AB

respectively such that the incenter of

A'B'C'

and

ABC

are coincide and the inradius of

A'B'C'

is half of inradius of

ABC

. Prove that

ABC

is equilateral .