IKMC 2016 - Grades 11-12 - Self-study Question 22

Question 22

A quadrilateral has an incircle tangent to all four sides. Its perimeter is in ratio 4:3 to the circle’s circumference. What is the ratio of their areas, quadrilateral : circle?

$4:\pi$
$3\sqrt2:\pi$
$16:9$
$\pi:3$
$4:3$