MathDB

Over the sides of an equilateral triangle with area

1

are triangles with the opposite angle

60^{\circ}

to each side drawn outside of the triangle. The new corners are

P

Q

and

R

. (and the new triangles

APB

BQC

and

ARC

) 1)What is the highest possible area of the triangle

PQR

? 2)What is the highest possible area of the triangle whose vertexes are the midpoints of the inscribed circles of the triangles

APB

BQC

and

ARC

Problem Statement