If two intersecting chords of a circle make equal angles with diameter passing through their point of intersection, prove that the chords are equal.

Every chord of a circle is a diameter.

Prove, by vector method or otherwise, that the point of intersection of the diagonals of a trapezium lies on the line passing through the midpoint of the parallel sides (you may assume that the trapezium is not a parallelogram).

The equation of the locus of the middle point of a chord of the circle x^2+y^2=2(x+y) such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally inclined to the x-axis is x+y=2 (b) x-y=2 2x-y=1 (d) none of these

L O L ' and M O M ' are two chords of parabola y^2=4a x with vertex A passing through a point O on its axis. Prove that the radical axis of the circles described on L L ' and M M ' as diameters passes though the vertex of the parabola.

Find the locus of the midpoint of chords of the parabola y^2=4a x that pass through the point (3a ,a)dot

Every diameter of a circle is a chord

Every chord of a circle contains exactly two points of the circle .

Two variable chords A Ba n dB C of a circle x^2+y^2=r^2 are such that A B=B C=r . Find the locus of the point of intersection of tangents at Aa n dCdot

Find the equation of the chord of the circle x^2+y^2=a^2 passing through the point (2, 3) farthest from the center.