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Preveina from Crest Girls' Academy sent us some pictures to support her reasoning about some of the shapes in this problem:
A circle can be always fitted in a square touching all 4 sides since the sides of a square are all equal. This makes the circle touch each side of the square evenly.
A circle can never be fitted in to a rectangle touching all 4 sides because a rectangle has 2 long sides and 2 short sides. When you're trying to draw a circle that touches all 4 sides in a rectangle it'll turn out to be an oval, since there are 2 long sides.
Circles in Quadrilaterals
Age 14 to 16
Challenge Level 
Preveina from Crest Girls' Academy sent us some pictures to support her reasoning about some of the shapes in this problem:
A circle can be always fitted in a square touching all 4 sides since the sides of a square are all equal. This makes the circle touch each side of the square evenly.
A circle can never be fitted in to a rectangle touching all 4 sides because a rectangle has 2 long sides and 2 short sides. When you're trying to draw a circle that touches all 4 sides in a rectangle it'll turn out to be an oval, since there are 2 long sides.
A circle can never be fitted in to a
parallelogram touching all 4 sides because a parallelogram has 2
long sides and 2 short sides just like a rectangle has.
A circle can also be fitted in to a
kite touching all 4 sides.
The circle can be sometimes fitted
into the trapezium touching all 4 sides depending on the length of
the sides. If the non-parallel sides are too far apart, the circle
becomes stretched into an oval.
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