In the previous problem, if O is the point on AD and `OO_(1)` is the perpendicular from the centre of the circle, `O_(-1), then OA//OD` will be

Options

A. `1`
B. `gt1`
C. `lt1`
D. depands upon `vec(B)` and charge

Explanation

To solve the problem step by step, let's analyze the information given and apply the principles of geometry and physics as discussed in the video transcript.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a point O on line AD.
- There is a perpendicular line drawn from the center of the circle (point O1) to point O, denoted as OO1.
- We need to find the ratio OA/OD.

2. **Identifying the Triangles**:
- The problem mentions two triangles: triangle OOO1 (formed by points O, O1, and the center of the circle) and triangle AOO1 (formed by points A, O, and O1).
- Since OO1 is perpendicular to AD, both triangles share the common side OO1.

3. **Congruent Triangles**:
- The triangles OOO1 and AOO1 are congruent. This can be established because:
- They share the side OO1.
- The angles at O (angle AOO1 and angle OOO1) are equal (both are right angles).
- The angles at O1 are also equal since they are subtended by the same line (the radius of the circle).
- By the criteria of congruence (Angle-Side-Angle), we conclude that these triangles are congruent.

4. **Establishing the Ratio**:
- Since the triangles are congruent, the corresponding sides are equal. Therefore:
- OA = OD
- This leads us to conclude that the ratio of OA to OD is:
\[ \frac{OA}{OD} = 1 \]

5. **Final Answer**:
- Thus, the final answer for the ratio OA/OD is:
\[ \boxed{1} \]