MathDB

1

Part of 2016 Bosnia and Herzegovina Team Selection Test

Problems(1)

Parallel lines and tangents

Source: Bosnia and Herzegovina TST 2016 day 1 problem 1

5/16/2016
Let ABCDABCD be a quadrilateral inscribed in circle kk. Lines ABAB and CDCD intersect at point EE such that AB=BEAB=BE. Let FF be the intersection point of tangents on circle kk in points BB and DD, respectively. If the lines ABAB and DFDF are parallel, prove that AA, CC and FF are collinear.
geometryTangentscircleparallelcollinear