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## 'Cyclic Quadrilaterals' printed from http://nrich.maths.org/

This problem invited students to
consider the relationship between opposite angles of cyclic
quadrilaterals. Often, with these types of problems, it is helpful
to draw diagrams; several students submitted diagrams as part of
their solution - well done.

The problem is divided into two parts: the
first part contains questions that form "building blocks" to help
meet the final challenge in the second part.

Nick, from St Stephen's at Carramar summed up
his solution:

The sum of the angles at opposite vertices
of a cyclic quadrilateral is $180^\circ$. This is the same for all
cyclic quadrilaterals, regardless of the positioning of the centre
dot.

Click here to see his full
solution with diagrams.

Well done also to the following students, who
also submitted similar (and correct!) answers to this problem:
Andre, Laura, Sascha, Chris and Sailesh from St. Stephen's School,
Marcus and Kye from St Philip's Primary School, and Natasha.

Now that you have completed this
problem, you could try the following problems as an
extension: Subtended Angles and/or Right Angles.