Proof:

Given: ∆ABC, AD ⊥ BC

To prove: AC^2 = AB^2 - 2BC * BD

Proof:
We will use the Pythagorean theorem and the properties of right triangles to prove the given statement.

Step 1:
Let's draw a diagram to visualize the given information.

∆ABC with AD ⊥ BC

```
A
/|
/ |
/ |
/ |
/ |
/ |
/ |
/ |
B-------D----C
```

Step 2:
Let's consider the right triangle ∆ABD. According to the Pythagorean theorem, we have:

AB^2 = AD^2 + BD^2 ...............(1)

Step 3:
Now, let's consider the right triangle ∆ACD. According to the Pythagorean theorem, we have:

AC^2 = AD^2 + CD^2 ...............(2)

Step 4:
Since AD ⊥ BC, we can conclude that CD = BD. Therefore, we can substitute CD with BD in equation (2):

AC^2 = AD^2 + BD^2 ...............(2)
= AD^2 + CD^2 ...............(2)
= AB^2 - BD^2 + CD^2 ...............(From equation (1))
= AB^2 - BD^2 + BD^2 ...............(Since CD = BD)
= AB^2

Step 5:
Hence, we have proven that AC^2 = AB^2 - 2BC * BD.

Conclusion:
In ∆ABC, with AD ⊥ BC, we have proved that AC^2 = AB^2 - 2BC * BD.