To find a possible midsegment length of the smaller triangle that is congruent to triangle \( ABC \) (with side lengths of 10, 16, and 23 units), we first need to understand the properties of midsegments in a triangle.
The midsegment connects the midpoints of two sides of the triangle and is parallel to the third side. The length of the midsegment is always half the length of the side to which it is parallel.
Since the original triangle has sides of lengths 10, 16, and 23 units, the midsegments corresponding to these sides would be:
- A midsegment parallel to the side of length 10 would have a length of \( 10 / 2 = 5 \) units.
- A midsegment parallel to the side of length 16 would have a length of \( 16 / 2 = 8 \) units.
- A midsegment parallel to the side of length 23 would have a length of \( 23 / 2 = 11.5 \) units.
Given the choices provided:
- 8 units
- 4 units
- 10 units
- 13 units
The only viable midsegment length from the smaller triangle, which maintains the relationship to the sides of the original triangle, is 8 units (which is half of 16 units).
Thus, a possible midsegment length of the smaller triangle is 8 units.