In a convex (10)-gon, no (3) diagonals meet at the same interior point. How many interior intersection points of diagonals are there?

Correct answer: (210)

In a convex polygon, an interior intersection of two diagonals is determined by four distinct vertices: the endpoints of one diagonal and the endpoints of the other. For any chosen set of four vertices, the two diagonals joining opposite vertices cross once inside the polygon. The condition that no three diagonals meet at one interior point ensures that different groups of four vertices do not represent the same intersection.

Thus we choose four vertices from ten, giving \(\binom{10}{4}=\frac{10\times9\times8\times7}{4\times3\times2\times1}=210\). Hence option B is correct. Counting pairs of diagonals directly would require care because some pairs may share endpoints; the four-vertex method avoids that issue and counts each interior crossing exactly once.