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 E`.

In Figure, equal chords A B and C D of a circle with centre O , cut at right angles at E . If M and N are mid-point of A B and C D respectively, prove that OMEN is a square.

If two chords A B and A C of a circle with centre O are such that the centre O lies on the bisector of /_B A C , prove that A B=A C , i.e. the chords are equal.

In a circle with centre O , chords A B\ a n d\ C D intersect inside the circumference at E . Prove that /_A O C+\ /_B O D=2\ /_A E C

In A B C ,A D is the median through A and E is the mid-point of A D . B E produced meets A C in F (Figure). Prove that A F=1/3A C .

In A B C ,A D is the median through A and E is the mid-point of A D . B E produced meets A C in F (Figure). Prove that A F=1/3A Cdot

In A B C ,A D is the median through A and E is the mid-point of A D . B E produced meets A C in F (Figure). Prove that A F=1/3A Cdot

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

In Figure, A B\ a n d\ A C are two equal chords of a circle whose centre is O . If O D\ _|_A B\ a n d\ O E\ _|_A C , prove that /_\A D E is an isosceles triangle.

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

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