P-intersection-point-of-bimedians-in-ABCD-convexe-quadrilateral-with-a-b-c-d-sides-e-f-diagonals-E-point-in-plane-x-y-z-t-distances-from-E-to-A-B-C-D-Prove-that-1-4-a-2-b-2-c-2-e-2-f-2-

Question Number 140785 by mathdanisur last updated on 12/May/21

P - i n t e r s e c t i o n p o i n t o f b i m e d i a n s i n

A B C D - c o n v e x e q u a d r i l a t e r a l w i t h

a; b; c; d - s i d e s, e; f - d i a g o n a l s,

E - p o i n t i n p l a n e, x; y; z; t - d i s t a n c e s

f r o m, E - t o A; B; C; D . P r o v e t h a t \dots

\frac{1}{4} (a^{2} + b^{2} + c^{2} + e^{2} + f^{2}) + 4 {P E}^{2} = x^{2} + y^{2} + z^{2} + t^{2}

Commented by mathdanisur last updated on 12/May/21

p l e a s e m r W S i r \dots

Commented by mr W last updated on 13/May/21

e a s y t o p r o v e w i t h v e c t o r m e t h o d .

s e e Q 140838

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