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MMO 011 Moscow MO 1935 sum of circumradii = another circumradius

Source:

July 17, 2019
circumradiusgeometryradiuscircumcircle

Problem Statement

In △ABC\vartriangle ABC, two straight lines drawn from an arbitrary point DD on ABAB are parallel to ACAC , BCBC and intersect BCBC , ACAC at FF , GG, respectively. Prove that the sum of the circumferences of the circles circumscribed around △ADG\vartriangle ADG and △BDF\vartriangle BDF is equal to the circumference of the circle circumscribed around △ABC\vartriangle ABC.
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