## Playing with Cyclic QuadrilateralsMay 27, 2011

Posted by Saketh in : bonus , trackback

Alex has created a model of a cyclic quadrilateral using some modelling clay. He observes that it has the following properties:

• It has a side of length $3$ and a side of length $5$.
• Its diagonals are perpendicular to each other.
• The sum of the lengths of its diagonals is $10$.

SeungIn sees a spider crawling on the model and attempts to swat it. Unfortunately, he ends up squishing the quadrilateral instead. Both of its diagonals shrink by exactly $1$ unit, but they remain perpendicular to each other. Determine the area of the new shape.