Reality is relative, not absolute.

Right, C.I. but we would do well to keep in mind that all those "constructs" are not just common to ALL humans (in one cultural form or another) but they are common ONLY TO HUMANS. We all "drink water" etc. and share all our constructions in order to live (i.e., many of them have survival value). That is the reality of our reality--we need culture--but that does not, according to the game-rules of metaphysics, make them really real. Philosophers like Wittgenstein, Nietzsche and Rorty (and I am tempted to include the Buddha) tell us not what is real; they liberate us from illusion by assisting us to know what is unreal. But they do not tell us that what is not real is necessarily unnecessary.

Of course there are common concepts of "persistent things" due to common perceptual apparatus, language and goals. But notice that we do not USE the word "reality" when engaged with such things unless there is significant disagreement about states of affairs.

E.g. Some say cycling is healthy, but the REALITY is, cyclists often have accidents.

What the layman does when asked (by a philosopher) to consider the term "reality" is to assume it refers to what he believes are non-controversial states of affairs despite the fact that he never normally uses the term "reality" in connection with them. The laymen usually does not understand the significance of philosophical issues like "meaning is use"(Wittgenstein) or anthropological issues like different words for "water" according to whether it is culturally taboo to drink it or not. Nor is the laymen likely to appreciate how words can shape thought (Sapir-Whorf) or how it can transmit aspects of social structure through gender norms in lexical selection. All this is implied in Rorty's citation of the term "social construction of reality".

LATER EDIT
Apologies to JLN for repeating some points due to delay in composition.

Fil, I assume that the rapid improvement in your use of English in the last couple of years is in part due to the editing of your posts. As such I think I should honor that progress by re-reading my last posts. Then you shoot the hell out of my beneficent motivation by declaring the brightest among us "retarded".

The reason the word reality is not used unless there is strong disagreement in opinion is precisely because what it refers to it is assumed to be a common frame of reference for all observers.

When I walk I don't question my walking.

"cycling as healthy versus dangerous" the reality of which is negotiable and relative to context in which the discussion takes place.

I see Frank has still got his putter upside down. No wonder the other clubs in the bag are a complete mystery to him !
(Remember the Beverly Hillbillies round the billiard table ? )

Okay I'll try once more.
It does not matter if a "state of affairs" is actually negotiated...it has to be potentially negotiable...the solution to a dilemma... for the word "reality" to be used. What you call a "fact" (from facere to construct) could equally well be stated.... (following a negotiation even with oneself)...
"the reality is that cycling is both healthy but potentially a risk to health".
Thus the negotiation results in a construction/resolution/description of a state of affairs concerning cycling, in which the word "reality" has functionality in decision making. Without such a node of negotiation the word "reality" is never used in normal life (excluding philosophy).
Now either you understand this point about usage or you do not. It may be counter-intuitive to you yet an examination of your own discourse will substantiate it.

Heidegger "Being and Time" (Sein und Zeit).

This is a useful introduction for non-readers.
http://www.youtube.com/watch?v=9P7bEoxpaM4