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Given two circles: O1 with radius r1, O2 with radius r2, where r1>r2. They are tangent to each other and mutually tangent to a common line.  If O1 is tangent to the line at point A and O2 tangent at point B, show that (AB)2 = 4r1r2. (Japanese "Temple Problem" 1892)

"Japanese ," Loci (March 2006)

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