`O A B C` is regular tetrahedron in which `D` is the circumcentre of ` O A B` and E is the midpoint of edge `A Cdot` Prove that `D E` is equal to half the edge of tetrahedron.

Explanation

To prove that \( DE \) is equal to half the edge of the tetrahedron \( OABC \), we will follow these steps:

### Step 1: Define Position Vectors
Let the position vectors of points \( O, A, B, C \) be represented as:
- \( \vec{O} = \vec{0} \) (origin)
- \( \vec{A} = \vec{a} \)
- \( \vec{B} = \vec{b} \)
- \( \vec{C} = \vec{c} \)
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