Show that in a quadrilateral ABCD `,AB+BC+CD+DA lt 2 (BD + AC)`

Explanation

To prove that in a quadrilateral ABCD, the inequality \( AB + BC + CD + DA < 2(BD + AC) \) holds, we can follow these steps:

### Step-by-Step Solution:

1. **Construct the Quadrilateral**:
Begin by sketching the quadrilateral ABCD. Label the vertices A, B, C, and D.

2. **Introduce a Point O**:
...