Question

These are numeric entry type questions.
A trapezium $ABCD$ is inscribed in a circle and PQRS is the quadrilateral formed by joining the midpoints of $AB,BC,CD$, and $DA$ in order. If $AC=$ $8cm$, then the perimeter of quadrilateral PQRS is_______ $cm$.

Answer 1

Answer: 16

In $△ABC,PQ=(1/2)AC$, and in $△ADC,SR$ $=(1/2)AC$.
$\therefore PQ+SR=AC$
In an isosceles trapezium, the diagonals are equal.
$\therefore SP+RQ=AC$
$\therefore PQ+QR+RS+SP=2AC=16cm$