Two equal chords `A B` and `C D` of a circle with centre `O ,` when produced meet at a point `E ,` as shown in Figure. Prove that `B E=D E` and `A E=C Edot`

Two equal chords AB and CD of a circle with centre O, when produced meet at a point E as shown in Figure,Prove that BE=DE and AE=CE.

In the figure,two equal chords AB and CD of a circle with centre O ,intersect each other at E , Prove that AD=CB

AB and CD are equal chords of a circle whose centre is O,when produced these chords meet at E,Prove that EB=ED

If two chords AB and AC of a circle with centre O are such that the centre O lies on the bisector of /_BAC, prove that AB=AC, i.e. the chords are equal.

In Figure, it is given that A E=A D and B D=C Edot Prove that A E B~=A D C

A B C D is a parallelogram. A D is a produced to E so that D E=D C and E C produced meets A B produced in Fdot Prove that B F=B Cdot

In Figure, it is given that A B=B C and A D=E C . Prove that A B E~=C B D

D a n d E are, respectively, the points on equal sides A B a n d A C of an isosceles triangle A B C such that B , C , E , a n d D are concyclic as shown in Figure. If O is the point of intersection of C D a n d B E , prove that A O is the bisector of line segment D E

A B C D is a cyclic quadrilateral. A Ba n dD C are produced to meet in Edot Prove that E B C-E D Adot

In Figure A B C D\ a n d\ A E F D are two parallelograms. Prove that: P E=F Q