  The Born rule provides a probability vector (distribution) with a quantum
state for a measurement setting. For two settings, we have a pair of vectors
from the same quantum state. Each pair forms a combined-probability vector that
obeys certain quantum constraints, which are triangle inequalities in our case.
Such a restricted set of combined vectors, titled combined-probability space,
is presented here for a $d$-level quantum system (qudit). The combined space
turns out a compact convex subset of a Euclidean space, and all its extreme
points come from a family of parametric curves. Considering a suitable concave
function on the combined space to estimate the uncertainty, we deliver an
uncertainty relation by finding its global minimum at the curves for a qudit.
If one chooses an appropriate concave (or convex) function, then there is no
need to search for the absolute minimum (maximum) on the whole space, it will
be at the parametric curves. So these curves are quite useful for establishing
an uncertainty (or a certainty) relation for a general pair of settings. In the
paper, we also demonstrate that many known tight (un)certainty relations for a
qubit can be obtained with the triangle inequalities.
