1977 AMC 12 Question 19
AMC12 · 1977 AMC 12
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
$PQRS$ is a parallelogram
$PQRS$ is a parallelogram if and only if $ABCD$ is a
rhombus
$PQRS$ is a parallelogram if and only if $ABCD$ is a
rectangle
$PQRS$ is a parallelogram if and only if $ABCD$ is a
parallelogram
none of the above are true