A point `O` is taken inside an equilateral four sided figure `A B C D` such that its distances from the angular points `D` and `B` are equal. Show that `A O` and `O C` are in one and the same straight line. GIVEN : A point `O` inside an equilateral quadrilateral four sided figure `A B C D` such that `B O=O Ddot` TO PROVE : `A O` and `O C` are in one and the same straight line.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the Given Information
We have an equilateral quadrilateral \( ABCD \) with a point \( O \) inside it such that the distances from \( O \) to points \( B \) and \( D \) are equal, i.e., \( OB = OD \).

### Step 2: Identify the Triangles
We will consider two triangles:
1. Triangle \( AOD \)
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