Question

The line joining the mid-points of two chords of a circle passes through its centre, then the chords are ______.

Options

• not parallel to each other

• equal to each other

• parallel to each other

• not equal to each other

Answer 1

The line joining the mid-points of two chords of a circle passes through its centre, then the chords are parallel to each other.

Explanation:

• Let the two chords be AB and CD. The line segment joining their mid-points passes through the centre O of the circle.
• The line drawn from the centre of a circle to the mid-point of a chord is perpendicular to the chord. Therefore, the line passing through the centre and the mid-points is perpendicular to both chords.
• Since both chords are perpendicular to the same line passing through the centre, they must be parallel to each other.