D is a point on the side BC of `triangleABC` such that `angleADC= angleBAC`, prove that `CA^(2)=CBxxCD`.

D is a point on the side BC of a triangle ABC such that /_A D C=/_B A C . Show that C A^2=C B.C D .

If D is a Point on the side BC of a Delta ABC such that AD bisects angleBAC . Then

P is any point inside the triangle ABC. Prove that : angleBPC gt angleBAC .

In figure, P is the mid-point of side BC of a parallelogram ABCD such that angleBAP=angleDAP . Prove that AD = 2CD.

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that A E^2+B D^2=A B^2+D E^2 .

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that A E^2+B D^2=A B^2+D E^2 .

In figure D is a point on side BC of a DeltaA B C such that (B D)/(C D)=(A B)/(A C) . Prove that AD is the bisector of /_B A C .

X and Y are points on the sides AB and BC respectively of triangleABC such that XY||AC and XY divides triangleABC into two parts in area , find (AX)/(AB)

In triangleABC , angleA= 60^(@) prove that BC^(2)= AB^(2)+AC^(2)- AB . AC

Lex X by any point on the side BC of a triangle ABC. If XM, XN are drawn parallel to BA and CA meeting CA, BA in M, N respectively; MN meets BC produced in T, prove that T X^2=T B x T C