Final answer:
The student's question is about adding the lengths of segments AD, CD, and BD in a geometric figure. Without more specific details, it is not possible to calculate the exact sum. Normally, such a question would involve applying principles like the triangle inequality theorem.
Step-by-step explanation:
The question given by the student involves the determination of the sum of the lengths of the segments AD, CD, and BD in a geometric figure. Since the lengths of ABC, ADC, ABD, and BDC are all provided, we are either dealing with a polygon or overlapping triangles. Without additional information such as the shape of the figure or relevant theorems, it's impossible to provide a precise numerical answer. In a typical polygon or triangle construction, you would either use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, or find a way to use the given lengths to determine the missing lengths through Pythagorean theorem or trigonometry.