Question

Two chords of a circle bisect each other. Then

• A. The chords are of equal length but less than the length of the diameter.
• B. The chords are of unequal length.
• C. The chords should be perpendicular bisectors of each other.
• D. The chords are any two diameters.

Answer 1

The correct option is D

The chords are any two diameters.

Let AB, CD be the chords intersecting at P such that AP = PB, CP = PD. As PC.PD = PA.PB, we get PA²=PC² or PA = PC. This means AB = CD, i.e., the chords are of equal length. The perpendicular to AB and CD at their midpoints pass through the centre of the circle.

Unless P is the centre of the circle this cannot happen. Thus AB and CD are diameters of the circle. They need not be mutually perpendicular. Thus option (D) is the correct one.