1. ## Paralellogram

Any cyclic paralellogram having unequal adjacent sides is necessarily a
(a)Square
(b)Rectangle
(c)Rhombus
(d)Trapezium
Why?

2. If a parallelogram is cyclic, then it must be a rectangle. The perpendicular bisectors of the sides of a parallelogram are concurrent only when it is a rectangle. For a parallelogram to be cyclic, its perpendicular bisectors must be concurrent at the center of the circumcircle; therefore, a cyclic parallelogram must be a rectangle.

3. Hello, devi!

Any cyclic paralellogram having unequal adjacent sides is necessarily a:
. . (a) square . (b) rectangle . (c) rhombus . (d) trapezium

This is my approach to this problem.
Perhaps you can hammer it into a formal proof.

Opposite sides of a parallelogram are parallel.
They are formed by a pair of parallel chords.
Code:
              * * *
*           *
*               *
A o o o o o o o o o o B

*                   *
*         *         *
D o o o o o o o o o o o C

*                 *
*               *
*           *
* * *

Opposite sides of a parallelogram are equal.
They are formed by two chords equidistant from the center.
Code:
              * * *
*           *
A o o o o o o o o o B
*        :        *
:
*         :         * C
*         *         o
*          \      o *
\   o
*            o    *
*         o     *
*     o     *
o * *
D

Since opposite sides of a parallelogram are parallel and equal,
the chords are parallel and equidistant from the center.
Code:
              * * *
*           *
A o o o o o o o o o B
*        :        *
:
*         :         *
*         *         *
*         :         *
:
*        :        *
D o o o o o o o o o C
*           *
* * *

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# any cyclic parallelogram having unequal adjacent sides

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