MathDB

10

Part of 2011 Sharygin Geometry Olympiad

Problems(1)

drawing parallels to diagonals of trapezoid, passing through intersection

Source: 2011 Sharygin Geometry Olympiad Correspondence Round P10

4/2/2019
The diagonals of trapezoid ABCDABCD meet at point OO. Point MM of lateral side CDCD and points P,QP, Q of bases BCBC and ADAD are such that segments MPMP and MQMQ are parallel to the diagonals of the trapezoid. Prove that line PQPQ passes through point OO.
geometrytrapezoiddiagonalsparallelIntersection diagonals