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Strange Rectangle

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Rectangle with quadrilateral drawn betweens points on each side.

Show that, for any values of $x$ and $y$ where $x> y$,

  1. the angle $SPQ$ is always the same and find this angle
  2. the angle $SRQ$ is always the same and find this angle
  3. the quadrilateral $SPQR$ is cyclic
  4. the angle $PQR$ is always the same and find this angle
  5. the angle $PSR$ is always the same and find this angle.