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1977 AMC 12 Question 19

AMC12 · 1977 AMC 12

Question 19

Let $E$ be the point of intersection of the diagonals of convex quadrilateral $ABCD,$ and let $P,$ $Q,$ $R$ and $S$ be the centers of the circles circumscribing triangles $ABE,$ $BCE,$ $CDE$ and $ADE,$ respectively. Then
  1. $PQRS$ is a parallelogram
  2. $PQRS$ is a parallelogram if and only if $ABCD$ is a
    rhombus
  3. $PQRS$ is a parallelogram if and only if $ABCD$ is a
    rectangle
  4. $PQRS$ is a parallelogram if and only if $ABCD$ is a
    parallelogram
  5. none of the above are true