Question

Two equal chords of a circle are always parallel.
A. True.
B. False.
C. Either.
D. Neither.

Answer 1

Hint: A chord of a circle is a line joining some two points on the circle.
Diameter is the longest chord possible in a circle.
A circle has infinitely many diameters and they are equal in length.

Complete step-by-step answer:
The following diagram shows two different possibilities for positions of two equal chords AB and CD.

In both the figures above, AB = CD. In the first figure, AB and CD are intersecting whereas $AB\parallel CD$ in the second figure.
It can be seen that the equal chords may be either parallel to each other or they may be intersecting as well.
Therefore, the statement of the question "Two equal chords of a circle are ALWAYS parallel." is definitely False, because it is possible for two equal chords to intersect as well.
Hence, the answer to the question is B. False.
Note: Consider the statement "Two equal chords of a circle are parallel.". This statement can be either True or False. But the statement "Two equal chords of a circle are always parallel." is definitely false because of the condition "always".
Equal chords of a circle are at equal distance from the center as well.
If two chords are equal and parallel, then they lie on opposite sides of the center.
A chord divides a circle into two parts which are called "segments" of the circle.