Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

A chord that passes through the centre of a circle is___

Prove that the line segment joining the points of contact of two parallel tangents of a circle, passes through its centre.

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

Prove that the segment joining the point of contact of two parallel tangents passes through the centre.

Prove that the perpendicular bisector of a chord of a circle always passes through the centre.

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.

Two circles with equal radii are intersecting at the points (1,0) and (-1,0) . Then tangent at the point (1,0) 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 line joining the mid-points of two parallel chords of a circle passes through the centre.

Perpendiculars are drawn,respectively,from the points P and Q to the chords of contact of the points Q and P with respect to a circle. Prove that the ratio of the length of perpendiculars is equal to the ratio of the distances of the points P and Q from the center of the circles.