MathDB

Let

A_1

and

B_1

be internal points lying on the sides

BC

and

AC

of the triangle

ABC

respectively and segments

AA_1

and

BB_1

meet at

O

. The areas of the triangles

AOB_1,AOB

and

BOA_1

are distinct prime numbers and the area of the quadrilateral

A_1OB_1C

is an integer. Find the least possible value of the area of the triangle

ABC

, and argue the existence of such a triangle.

Problem Statement