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fig
Two semi-circles are drawn on one side of a line segment. Another semi-circle touches them externally as shown in the diagram.
 
What is the radius of the circle that touches all three semi-circles in terms of the radii of the first two semi-circles?

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Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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