Geometry · Squares · Tangent circles · Diagonals · Lengths along a line · Rationalisation
The figure shows two squares and two congruent circles whose centres lie on a diagonal of the larger square. The smaller square occupies a corner of the larger one, and the diagonal in question runs from that corner to the opposite one. The two circles touch each other; the circle nearer the far corner touches both sides of the larger square that meet there, and the other circle passes through the far corner of the smaller square. The larger square has side \(1\), and the side of the smaller square is twice the radius of the circles.
Compute the radius of the circles and give the answer with a rationalised denominator.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), odbirno (qualifying) round 2021, 1. letnik, category A, problem 1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source