Problem

Source: 2023 Israel National Olympiad P5

Tags: geometry, geometric inequality, rectangle



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.


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