Into the Pyramid

Geometry Level 3

The diagram above shows a triangular pyramid with equal edges and faces, and \(A, B, C, D\) are its vertices.

Let \(E\) be the midpoint of \(AB\), \(O\) be the center of the equilateral triangle base, and \(P\) be the center of the 3-D pyramid.

What are the ratios of \(CO : OE\) and \(DP : PO\) respectively?

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