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ST \ge 2r(\sqrt{2}-1) , inscribed circles in a semicircle

Source: 1997 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p3

January 27, 2020
geometrycirclessemicircle

Problem Statement

A semicircle with diameter AB=2rAB = 2r is divided into two sectors by an arbitrary radius. To each of the sectors a circle is inscribed. These two circles touch ABB at SS and TT. Show that ST≥2r(2−1)ST \ge 2r(\sqrt{2}-1).
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