MathDB

3

Part of 2018 Finnish National High School Mathematics Comp

Problems(1)

butterfly theorem in finnish high school math competition

Source: Finland 2018, p3

9/8/2019
The chords ABAB and CDCD of a circle intersect at MM, which is the midpoint of the chord PQPQ. The points XX and YY are the intersections of the segments ADAD and PQPQ, respectively, and BCBC and PQPQ, respectively. Show that MM is the midpoint of XYXY.
geometryChordsmidpointcircle