E is the mid-point of a median AD of ∆ABC and BE is produced to meet AC at F.Determine the value of AF.

The problem is based on the properties of medians in a triangle.

Step 1: Given that E is the midpoint of the median AD of triangle ABC.

Step 2: According to the property of medians, the line segment joining the vertex of a triangle to the midpoint of its opposite side is called a median. The median divides the triangle into two triangles of equal areas.

Step 3: Also, given that BE is produced to meet AC at F.

Step 4: According to the property of medians, the point where the medians of a triangle intersect divides each median in the ratio 2:1, where the centroid is 2/3 of the distance from the vertex to the midpoint of the opposite side.

Step 5: Therefore, since E is the midpoint of AD, it is 2/3 of the distance from A to D.

Step 6: Since BE is extended to F, AF is the remaining 1/3 of AD.

Step 7: Therefore, the value of AF is 1/3 of AD.