O হল একটি আয়তক্ষেত্র ABCD-এর ভিতরের যেকোনো বিন্দু। প্রমাণ করুন যে `OB^2+OD^2=OA^2+OC^2`....

The OABC is a tetrahedron such that OA^2+BC^2=OB^2+CA^2=OC^2+AB^2 ,then

O is any point inside a rectangle ABCD.Prove that OB^(2)+OD^(2)=OA^(2)+OC^(2)

O is any point inside a rectangle ABCD. Prove that OB^(2)+OD^(2)=OA^(2)+OC^(2) . DEDUCTION In the given figure, O is a point inside a rectangle ABCD such that OB=6cm, OD=8 cm and OA=5 cm, find the length of OC.

If G be the centroid of the DeltaABC and O be any other point in theplane of the triangle ABC , then prove that: OA^2 +OB^2 +OC^2=GA^2 +GB^2 +GB^2 + GC^2 + 3GO^2

If OABC is a tetrahedron such that OA^(2)+BC^(2)=OB^(2)+CA^(2)=OC^(2)+AB^(2) then

If OABC is a tetrahedron such that OA^(2)+BC^(2)=OB^(2)+CA^(2)=OC^(2)+AB^(2) then

A point O in the interior of a rectangle ABCD is joined with each of the vertices A,B,B,C and D. Prove that OB^(2)+OD^(2)=OC^(2)+OA^(2)

O is a point in the interior of Delta ABC, OD bot BC, OE bot AC and OF bot AB , as shown in the figure, Prove that : (i) OA^(2)+OB^(2)+OC^(2)-OD^(2)-OE^(2)-OF^(2)=AF^(2)+BD^(2)+CE^(2) (ii) AF^(2)+BD^(2)+CE^(2)=AD^(2)+BF^(2)+CD^(2)

From a point O in the interior of a ABC, perpendiculars OD,OE and OF are drawn to the sides BC,CA and AB respectively. Prove that: (i) AF^(2)+BD^(2)+CE^(2)=OA^(2)+OB^(2)+OC^(2)-OD^(2)-OE^(2)-OF^(2) (ii) AF^(2)+BD^(2)+CE^(2)=AE^(2)+CD^(2)+BF^(2)