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Find the radius r of the two equal circles

Source: Baltic Way 1993

June 15, 2012
geometry unsolvedgeometry

Problem Statement

Two circles, both with the same radius rr, are placed in the plane without intersecting each other. A line in the plane intersects the first circle at the points A,BA,B and the other at points C,DC,D, so that ∣AB∣=∣BC∣=∣CD∣=14cm|AB|=|BC|=|CD|=14\text{cm}. Another line intersects the circles at E,FE,F, respectively G,HG,H so that ∣EF∣=∣FG∣=∣GH∣=6cm|EF|=|FG|=|GH|=6\text{cm}. Find the radius rr.
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