If two chords of a circle intersect inside or outside the circle when produced ; the rectangle formed by the two segments of one chord is equal in area to the rectangle formed by the two segments of the other chord.

Theorem of internal division of chords. Suppose two chords of a circle intersect each other in the interior of the circle, then the product of the lengths of the two segments of one chord is equal to the product of the lengths of the two segments of the other chord. Given : (1) A circle with centre O . (2) chords PR and QS intersect at point E inside the circle. To prove : PE xx ER = QE xx ES Construction : Draw seg PQ and seg RS

If two equal chords of a circle intersect within the circle,prove that the segments of one chord are equal to corresponding segments of the other chord.

If the two equal chords of a circle intersect : (i) inside (ii) on (iii) outside the circle, then show that the line segment joining the point of intersection to the centre of the circle will bisect the angle between the chords.

If two equal chords of a circle intersect within the circle,prove that 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.

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.

The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends in the major segment of the circle is equal to :

If two chords of a congruent circle are equal; then their corresponding arcs.