MathDB

Consider a triangle

ABC

in which

AB<BC<CA

. The excircles touch the sides

BC, CA,

and

AB

at points

A_1, B_1

and

C_1

respectively. A circle is drawn through the points

A_1, B_1

and

C_1

which intersects the sides

BC, CA

and

AB

for the second time at the points

A_2, B_2

and

C_2

respectively. On which side of the triangle can lie the largest of the segments

A_1A_2, B_1B_2

and

C_1C_2

?
Proposed by I. Weinstein

Problem Statement