In Fig. 2.54, o is a point in the interior of a triangle `ABC,ODbotBC,OEbotACandofbotAB.` Show that
`OA^(2)+OB^(2)+OC^(2)-OD^(2)-OE^(2)-OF^(2)=AF^(2)+BD^(2)+CE^(2),`

In Fig. 2.54, o is a point in the interior of a triangle ABC,ODbotBC,OEbotACandofbotAB. Show that AF^(2)+BD^(2)+CE^(2)=AE^(2)+CD^(2)+BF^(2).

In the figure given below, O is point in the interior of a triangle ABC, OD _|_ BC , OE _|_ AC and OF _|_ AB . Show that (i) OA^(2) + OB^(2) + OC^(2) + OD^(2) - OE^(2) - OF^(2) = AR^(2) + BD^(2) + CE^(2) (ii) AF^(2) + BD^(2) + CE^(2) = AE^(2) + CD^(2) + BF^(2)

D is a point on the side BC of a triangle ABC such that angleADC=angleBAC . Show CA^(2)=CB.CD

In Fig . AD is a median of a triangle ABD and AM bot BC. Prove that : AC^(2)+AB^(2)=2AD^(2)+1/2 BC^(2)

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

In Fig . AD is a median of a triangle ABD and AM bot BC. Prove that : AB^(2)=AD^(2)-BC.DM+((BC)/(2))^(2)

In Fig . AD is a median of a triangle ABD and AM bot BC. Prove that : AC^(2)=AD^(2)+BC. DM+((BC)/(2))^(2)

If A , B and C are interior angles of a triangle ABC, then show that tan ((A+B) /(2)) =cot C/(2)

In Fig . ABC is a triangle in which angleABClt90^(@)and AD botBC. Prove that AC^(2)=AB^(2)+BC^(2)-2BC.BD.