In Figure, `X ,\ Y\ ` are two points on equal sides `A B\ a n d\ A C` of a ` A B C` such that `A X=A Ydot` Prove that `X C=Y B`

In Figure, X and Y are two points on equal sides A B and A C of a A B C such that A X=A Ydot Prove that X C=Y Bdot

In Figure, A C > A B\ a n d\ D is the point on A C such that A B=A Ddot Prove that B C > C D

D and E are points on equal sides A B and A C of an isosceles triangle A B C such that A D=A E . Prove that B ,C ,D ,E are concylic.

A B C D is a square, X\ a n d\ Y are points on sides A D\ a n d\ B C respectively such that A Y=B X . Prove that B Y=A X\ a n d\ /_B A Y=/_A B X

In Figure, X ,\ Y are the mid-points of opposite sides A B\ a n d\ D C of a parallelogram A B C D. A Y\ a n d\ D X are joined intersecting in P ; C X\ a n d\ B Y are joined intersecting in Q . Show that (i) A X C Y is a parallelogram (ii) D X B Y\ is a parallelogram (iii) P X Q Y is a parallelogram

In Figure, X ,Y are the mid-points of opposite sides A B and D C of a parallelogram A B C Ddot A Y and D X are joined intersecting in P ; C X and B Y are joined intersecting in Qdot Show that DXBY is a parallelogram, P X Q Y is parallelogram.

In Figure, A B C D is a parallelogram and X\ a n d\ Y are points on the diagonal B D such that D X=B Y . Prove that A X C Y is a parallelogram (ii) A X=C Y ,\ A Y=C X A Y B\ ~= C X D (iv) A X D~=\ C Y B

In Figure, A B C D is a parallelogram and X\ a n d\ Y are points on the diagonal B D such that D X=B Y . Prove that A X C Y is a parallelogram (ii) A X=C Y ,\ A Y=C X (iii) A Y B\ ~= C X D (iv) A X D~=\ C Y B

In Figure, X\ a n d\ Y are the mid-points of A C\ a n d\ A B respectively, Q P || B C\ a n d\ C Y Q\ a n d\ B X P are straight lines. Prove that a r\ (\ A B P)=\ a r\ (\ A C Q) .

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 .