MathDB

Let

ABC

be an equilateral triangle whose sides have length

1

. The midpoints of

AB,BC

are

M,N

respectively. Points

K,L

were chosen on

AC

so that

KLMN

is a rectangle. Inside this rectangle are three semi-circles with the same radius, as in the picture (the endpoints are on the edges of the rectangle, and the arcs are tangent). Find the minimum possible value of the radii of the semi-circles.

Problem Statement