MathDB
Trapezoid and circles

Source: Centroamerican Olympiad 2014, problem 2

June 10, 2014
geometrytrapezoidgeometry proposed

Problem Statement

Let ABCDABCD be a trapezoid with bases ABAB and CDCD, inscribed in a circle of center OO. Let PP be the intersection of the lines BCBC and ADAD. A circle through OO and PP intersects the segments BCBC and ADAD at interior points FF and GG, respectively. Show that BF=DGBF=DG.
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