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 $AC =$ $8 cm$, then the perimeter of quadrilateral PQRS is_______ $cm$.

Answer 1

In $\triangle ABC , PQ =(1 / 2) AC$, and in $\triangle ADC , SR$ $=(1 / 2) AC$.
$\therefore PQ + SR = AC$
In an isosceles trapezium, the diagonals are equal.
$\therefore S P+R Q=A C $
$\therefore P Q+Q R+R S+S P=2 A C=16 cm$