(i) OABC is a regular tetrahedron D is circumcentre of Δ OAB and E is mid point of edge AC.
Prove that DE is equal to half the edge of tetrahedron.
(ii) If V be the volume of a tetrahedron and V ′ be the volume of the tetrahedron formed by the centroids and V = k V ′ then find the value of k.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i)
= 
( Δ OAB is an equilateral Δ )
∴ 
= 
( 
= 
= 
and θ = 60°)
⇒ DE = 
⇒ DE = 
⇒ DE = 
(ii) V = 
The centroid are 
, 
, 
, 
∴ V ′ = 
= 
= 
V ∴ k = 27
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