Triangle Median Problem: Finding AC Length When BC = AC

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information that $AD$ is the median making $BD = CD = 5$.
• Step 2: Use the triangle property that $BC = AC$ as per the problem’s isosceles condition.
• Step 3: Calculate $BC = BD + CD = 5 + 5 = 10$.
• Step 4: Since $BC = AC$, by isosceles property, conclude $AC = 10$.

Now, let's work through each step:
Step 1: With $AD$ as the median, it divides $BC$ into $BD = 5$ and $CD = 5$.
Step 2: The condition $BC = AC$ ensures the triangle is isosceles.
Step 3: Calculate $BC$ as $BD + CD = 5 + 5 = 10$.
Step 4: Since $BC = AC$, therefore, $AC = 10$.

Therefore, the length of $AC$ is $10$.