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

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

In the given fig DeltaDGH~DeltaDEF, DH=8cm, DF=12cm, DG=(3x-1) cm and DE=(4x+2) cm, Find the lengths of DG and DE. OR D is a point on the side BC of DeltaABC such that lfloorADC=lfloorBAC . Prove that (CA)/(CD)=(CB)/(CA) .

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).

If D is the mid-point of side BC of a triangle ABC and AD is perpendicular to AC, then

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).

D and E are points on sides AB and AC respectively of tirangle ABC such that ar (DBC) = ar (EBC) . Prove that DE || BC

In Fig .D is a point on side BC of DeltaABC such that (BD)/(CD) =(AB)/(AC) prove that AD is the bisector of angleBAC.

If D, E and F are three points on the sides BC, CA and AB, respectively, of a triangle ABC such that the lines AD, BE and CF are concurrent, then show that " "(BD)/(CD)*(CE)/(AE)*(AF)/(BF)=-1

D and E are points on sides AB and AC respectively of Delta ABC such that ar (DBC) = ar EBC). Prove that DE |\| BC.