ABCD is a rhombus. Prove that `AB^(2)+BC^(2)+CD^(2)+DA^(2)= AC^(2)+BD^(2)`.

ABC is a right triangle right angled at B. Let D and E be any points on AB and BC respectively. Prove that AE^(2) + CD^(2) = AC^(2) + DE^(2) .

In the given figure, AD is a median of a DeltaABC and AM bot BC . Prove that : AC^(2)+AB^(2)= 2AD^(2)+(1)/(2) BC^(2)

In triangleABC , AD, BE, CF are the medians. Prove that, 4(AD^(2)+BE^(2)+CF^(2))= 3(AB^(2)+BC^(2)+AC^(2)) .

In a right triangle ABC right angled at C, P and Q are points on sides AC and CB respectively which divide these sides in the ratio of 2 : 1. Prove that (i) 9 AQ^(2) = 9AC^(2) + 4BC^(2) (ii) 9BP^(2) = 9BC^(2) + 4AC^(2) (iii) 9 (AQ^(2) + BP^(2)) = 13 AB^(2)

In DeltaABC, /_B=90^(@) . D and E are any points on sides AB and BC respectively. Prove that AE^(2)+CD^(2)= AC^(2)+DE^(2) .

In the given figure, O is a point in the interior of a DeltaABC, OD bot BC, OE bot AC" and "OF bot AB . Show that : AF^(2)+BD^(2)+CE^(2)=AE^(2)+CD^(2)+BF^(2) .

‘O’ is any point in the interior of a triangle ABC. If OD bot BC, OE bot AC and OF bot AB, show 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) = AE^(2) + CD^(2) + BE^(2) .

In the given figure, O is a point in the interior of a DeltaABC, OD bot BC, OE bot AC" and "OF bot AB . Show that : OA^(2)+OB^(2)+OC^(2)-OD^(2)-OE^(2)-OF^(2)= AF^(2)+BD^(2)+CE^(2) .

D and E are points on the sides CA and CB respectively of a DeltaABC right angled at C. Prove that AE^(2)+BD^(2)= AB^(2)+DE^(2) .