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 need to show that lines \(AO\) and \(OC\) are in the same straight line given that point \(O\) is inside an equilateral quadrilateral \(ABCD\) and the distances from \(O\) to points \(B\) and \(D\) are equal.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We have an equilateral quadrilateral \(ABCD\) where \(AB = BC = CD = DA\).
- Point \(O\) is inside the quadrilateral such that \(OB = OD\).

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