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'Circles in Quadrilaterals' printed from http://nrich.maths.org/
You may have come across the idea of a cyclic quadrilateral, where
it is possible to draw a circle around the quadrilateral so that
the circumference passes through all four points.
A tangential quadrilateral is one where it is possible to draw a
circle inside it so that the circumference just touches all four
sides of the shape.
Here are some examples of tangential quadrilaterals:
For each of the following types of quadrilaterals, decide
whether it is always, sometimes or never possible to construct a
circle inside which just touches all four sides.
If you decide always or never, you need to justify your
decision with a convincing argument.
If you decide sometimes you need to be precise about when it
is possible and when it is not possible, and why.
Send us your explanations and justifications, and anything else
of interest you discover about these special quadrilaterals!