If a line is drawn through the centre of a circle to bisect a chord, then prove that it is perpendicular to the chord.

Statement I The lines from the vertex to the two extremities of a focal chord of the parabola y^2=4ax are perpendicular to each other. Statement II If extremities of focal chord of a parabola are (at_1^2,2at_1) and (at_2^2,2at_2) , then t_1t_2=-1 .

If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.

In the figure, ‘O’ is the centre of the circle and OM, ON are the perpendiculars from the centre to the chords PQ and RS. If OM = ON and PQ = 6cm. Find RS

If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

How many chords can be drawn through 21 points on a circle?

A point P is at the 9 unit distance from the centre of a circle of radius 15 units. The total number of different chords of the circle passing through point P and have integral length is

Using therem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in class IX).

In a circle with centre 'O' . bar(AB) is a chord and 'M' is its midpoint . Now prove that angle (OM) is perpendicular to AB

The longest chord of a circle is a ......... of the circle.

Prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side (Using basic proportionality theorem).