Prove that the perpendicualr bisector of any chord of a circle passes thorugh the centre of the circle .

The perpendicular bisector of any chord of a circle passes through the ____________ of that circle .

Fill in the blanks The perpendicular bisector of any chord of a circle is passed through the ______of the circle.

Write True or False Perpendicular bisectors of two chords of a circle, which are not the diameters, meet at the centre of the circle.

If the angle - bisector of two intersecting chords of a circle passes through its centre , then prove that the chords are equal .

Prove that two equal chords are equidistant from the centre of the circle.

The two chords AB and AC of a circle are equal, prove that the bisector, of angleBAC passes through the centre of the circle.

Prove that the internal bisector of the angle between two tangents drawn from an external point of a circle will pass through the centre of the circle.

Two circles with equal radii are intersecting at the points (0, 1) and (0,-1). The tangent at the point (0,1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is.

Prove that the internal bisector of any angle of a cyclic quadrilateral and the external bisector of its opposite angle intersect each other on the circumference of the circle.

Prove that the lengths of the chord of a circle which subtends an angle 108^(@) at the centre is equal to the sum of the lenths of the chords which subtend angles 36^(@) and 60^(@) at the centre of the same circle.