Let `A_(1)A_(2)A_(3)………………. A_(14)` be a regular polygon with 14 sides inscribed in a circle of radius 7 cm. Then the value of `(A_(1)A_(3))^(2) +(A_(1)A_(7))^(2) + (A_(3)A_(7))^(2)` (in square cm) is……………..

Explanation

To solve the problem, we need to find the value of \( (A_1A_3)^2 + (A_1A_7)^2 + (A_3A_7)^2 \) for a regular polygon with 14 sides inscribed in a circle of radius 7 cm.

### Step-by-Step Solution:

1. **Understanding the Geometry**:
- We have a regular polygon with 14 sides inscribed in a circle of radius \( r = 7 \) cm.
- The vertices of the polygon can be denoted as \( A_1, A_2, A_3, \ldots, A_{14} \).
- The angle subtended by each side at the center of the circle is \( \frac{2\pi}{14} = \frac{\pi}{7} \).
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