(Converse of Theorem 3) The line joining the centre of a circle to the mid-point of a chord is perpendicular to the chord.

The given figure shows a circle with centre O. P is mid-point of chord AB. Show that OP is perpendicular to AB.

prove that the line joining the mid-point of two equal chords of a circle subtends equal angles with the chord.

The perpendicular from the centre of a circle to a chord bisects the chord.

Prove that the line joining the mid-point of a chord to the centre of the circle passes through the mid-point of the corresponding minor arc.

If two equal chords of a circle in intersect within the circle, prove that : the segments of the chord are equal to the corresponding segments of the other chord. the line joining the point of intersection to the centre makes equal angles with the chords.

If two equal chords of a circle in intersect within the circle, prove that: the segments of the chord are equal to the corresponding segments of the other chord. the line joining the point of intersection to the centre makes equal angles with the chords.

Describe : The locus of the mid-points of all chords parallel to a given chord of a circle.

Find the locus of the centre of the circle passing through the vertex and the mid-points of perpendicular chords from the vertex of the parabola y^2 =4ax .

2 parallel chords 24 cm, and 18 cm, are on the same side of the centre of a circle. If the distance between the chords is 3 cm, calculate the radius of the circle.

Prove that the line joining the mid-points of two parallel chords of a circle passes through the centre.