Cyclic Quadrilaterals are often important objects in a Geometry problem. Recognizing them can lead to a path to the solution. A case in point is this problem from Pre RMO 2017.

How to recognize cyclic quadrilaterals? 

  • Opposite angles add up to \( \pi \)
  • Two angles subtended by one segment are equal
  • Sum of the product of opposite sides equal product of diagonals

Now look into this problem:

Part 1

Part 2

Part 3