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

Equal chords of a circle subtend equal angles at the centre.

If two chords of a circle bisect one another they must be diameters.

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 chord.

Is every chord of a circle also a diameter?

Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonals.

If a diameter of a cirlce bisects each of the chords of the circle, prove that the chordds are parallel.

Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.

PQ and RQ are chords of a circle equidistant from the centre. Prove that the diameter passing through Q bisects anglePQR