`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.

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A Ddot Prove that area of B E D=1/4a r e aof A B Cdot GIVEN : A A B C ,D is the mid-point of B C and E is the mid-point of the median A Ddot TO PROVE : a r( B E D)=1/4a r( A B C)dot

A B C is a triangle. D is a point on A B such that A D=1/4A B and E is a point on A C such that A E=1/4A Cdot Prove that D E=1/4B Cdot

A B C is a triangle. D is a point on A B such that D=1/4A B\ a n d\ E is a point on A C such that A E=1/4A Cdot Prove that D E=1/4B C

In Figure, A D is the median and D E||A B . Prove that B E is the median.

D is the mid-point of side B C of A B C and E is the mid-point of B Ddot If O is the mid-point of A E , prove that a r( B O E)=1/8a r( A B C)

IF OABC is a tetrahedron where O is the origin and A,B and C have respective positions vectors as bara,barb and barc then prove that the circumcentre of the tetrahedron is ((bara)^2(barb times barc)+(barb)^2 (barc times bara)+(barc)^2 (bara times barb))/(2[bara barb barc])

In Figure, it is given that A E=A D and B D=C Edot Prove that A E B~=A D C

OABC is a tetrahedron D and E are the mid points of the edges vec OA and vec BC. Then the vector vec DE in terms of vec OA,vec OB and vec OC

Regular tetrahedron a tetrahedron whose all the edges are of equal length is called a regular tetrahedron.

Prove that any two opposite edges in a regular tetrahedron are perpendicular.