From a point O in the interior of triangle 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

From a point O in the interior of triangle ABC, perpendiculars OD, OE

1.	From a point O in the interior of triangle 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
Answer» From a point O in the interior of triangle 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