Bidyut Guha Thakurta and Amitava Mitra Solutions for Exercise 1: EXERCISE 1

The chords $\mathrm{AB}$ and $\mathrm{CD}$ of a circle with its centre at $\mathrm{O}$ are congruent. If $\mathrm{OX}\perp \mathrm{AB}$ and $\mathrm{OY}\perp \mathrm{CD}$, then $\mathrm{BX}=\mathrm{CY}$.

The chords $\mathrm{AB}$ and $\mathrm{CD}$ of a circle with its centre at $\mathrm{O}$ are congruent. If $\mathrm{OX}\perp \mathrm{AB}$ and $\mathrm{OY}\perp \mathrm{CD}$, then $\mathrm{CD}=\mathrm{AX}$.

The chords $\mathrm{AB}$ and $\mathrm{CD}$ of a circle with its centre at $\mathrm{O}$ are congruent. If $\mathrm{OX}\perp \mathrm{AB}$ and $\mathrm{OY}\perp \mathrm{CD}$, then $\mathrm{OX}=\mathrm{OY}$.

Two diameters of a circle can never be parallel to each other.

Two chords of a circle can never be parallel to each other.

A diameter perpendicular to a chord of a circle bisects the chord.

Diameter is the greatest chord of a circle.

True or false :

Circumference is the greatest arc of a circle.