Can you use the key properties of cyclic quadrilaterals to find quick solution paths on certain AMC problems?

The interior angles of cyclic quadrilaterals have certain important properties. The opposite ones sum to $180_{o}$, for example. But there are important lesser-known properties as well, involving the angles formed by the diagonals of the cyclic quadrilateral.

The lengths of the diagonals are also constrained in a super-interesting way: their product is equal to the sum of the products of the opposite sides of the quadrilateral. (This seems a little crazy until you consider how this might be related to the Pythagorean theorem.)

Even the area of a c.q. has a formula associated with it. (It’s like Heron’s formula for triangles: it gives the area of a c.q. in terms of the lengths of its sides only.)

These facts are all covered in the quizzes for this section.

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