Triangle Median Problem: When BD = 1/2 AC, Is ABC Right?

In this problem, we are given that $BD$ is the median of triangle $\triangle ABC$ and that $BD$ is half the length of side $AC$. We want to determine if $\triangle ABC$ is a right triangle.

By the properties of triangles, if the median ($BD$) from the vertex to the hypotenuse ($AC$) of a triangle is half the length of the hypotenuse ($AC$), then the triangle is right-angled.

The key property here is that in a right triangle, the median to the hypotenuse is half the hypotenuse. This median property is a unique characteristic for right triangles.

Thus, since $BD = \frac{1}{2}AC$ and $BD$ is the median, we conclude that triangle $\triangle ABC$ is indeed a right triangle.

Therefore, the solution to the problem is: Yes, $\triangle ABC$ is a right triangle.