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

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

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 line joining the mid-points of two parallel chords of a circle passes through the centre.

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

If two circles touch each other (internally or externally); the point of contact lies on the line through the centres.

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:

If a chord is drawn through the point of contact of a tangent to a circle; then the angle which this chord makes with the given tangent are equal respectively to the angles formed in the corresponding alternate segments.