# Ptolemy and Cyclic Quadrilaterals

- Author:
- Esther Gruenhut

- Topic:
- Quadrilaterals

## Prove that the product of the diagonals is the sum of the product of the pairs of opposite sides

## Proof:

1. Explain the construction
2. Prove that the triangles in the first pair are similar.
3. Prove that the triangles in the second pair are similar.
4. Write out the proportions deduced from the above steps
5. Finish the proof
(solution at the bottom of this page)