Prove that the bisectors of the angles in the segment of a circle pass through a common point.

Angles in the same segment of a circle are equal

Prove that angles in the same segment of a circle are equal.

All angles in the same segment of a circle are __________

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

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

In the parallelogram ABCD , AB = 2AD . Prove that the bisectors of the angles angleBAD and angleABC meet at the mid-point of DC at right -angles.

Show that the circle x^(2) + y^(2) + 4(x+y) + 4 = 0 touches the coordinates axes. Also find the equation of the circle which passes through the common points of intersection of the above circle and the straight line x+y+2 = 0 and which also passes through the origin.

Show that the circle x^(2) + y^(2) + 6(x-y) + 9 = 0 touches the coordinates axes. Also find the equation of the circle which passes through the common points of intersection of the above circle and the straight line x-y+4 = 0 and which also passes through the origin.

Answer any one question : Prove that angles in the same segment of a circle are equal.