Final Answer:
AC = 6
Step-by-step explanation:
Points B and C lie on AD, and we are given that point C is the midpoint of BD (BC = CD). Additionally, BD is given as 14, and AB is expressed as DC - 5. To find AC, we need to consider the relationships between the lengths of the segments in the given scenario.
Let's denote the length of BC as x. Since C is the midpoint of BD, and BD is given as 14, we have BC = CD = x, and BD = 14. Therefore, x + x = 14, which simplifies to 2x = 14. Solving for x, we find that x = 7.
Now, we know the lengths of BC and CD. Since AB is expressed as DC - 5, and DC is equal to x (which is 7), we can calculate AB as 7 - 5 = 2.
Finally, to find AC, we add the lengths of AB and BC: AC = AB + BC = 2 + 7 = 9. Therefore, the final answer is AC = 9.
In conclusion, the key relationships in this problem involve the midpoint property of BC and CD, along with the given lengths of BD and the expression for AB.
By carefully considering these relationships and solving for the required lengths, we arrive at the final answer, AC = 9.