Why do this problem?
This problem is all about geometrical reasoning and proof.
It gives learners the opportunity to play with a problem and
come up with a conjecture from practical demonstrations, and
then justify their findings. It also opens up discussion of
when it is necessary to write something as a strict inequality.
Possible approach
This problem lends itself to investigation with a dynamic
geometry tool such as Geogebra.
The learners could start by constructing a quadrilateral on a
unit circle, and displaying the lengths of each side. The
challenge is to make the shortest side as long as possible.
Once the length has been found, learners need to come up with a
convincing argument that it is not possible for the shortest
side to be any longer.
Learners could then discuss in pairs the best way of making
the second side as large as possible. What happens to the
shortest side in this process? The question says "Side $b$ must
be less than a certain value" so there is the opportunity to
discuss why it has to be strictly less than that value and can
never actually reach it.
The last part of the question encourages discussion along similar
lines. It is good to bring out of the discussion that the third
side can be as close to $2$ units as you wish but can never
actually be exactly $2$.
Key questions
If I move the points on the circumference to increase one of
the sides, what will happen to the adjacent side?
What shape should I make in order to make the shortest side as
long as possible?
Possible extension
The same problem could be tackled as a
hexagon on the circumference of a circle, rather than a
quadrilateral.
Possible support
Start by considering a triangle on the
circumference of a circle and calculate the maximum and minimum
side lengths.