A queen is placed at the centre of carom-board which has side of length a . It is hit from a position with a striker such that after rebounding from the front end, it goes into the hole in the opposite end. Find the distance traveled by the queen

Explanation

To solve the problem of finding the distance traveled by the queen on a carom board, we can break it down into a series of steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- The carom board is a square with side length \( a \).
- The queen is placed at the center of the board, which is at the coordinates \( \left(\frac{a}{2}, \frac{a}{2}\right) \).
- The queen is hit by a striker and rebounds off one edge of the board before going into the opposite hole.
...