Prove that if any straight line passing through the centre of a circle bisects any chord, which is not a diameter, then the straight line will be perpendicular on that chord.

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

(xv) Which one of the following straight line passes through the origin ?

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

Find the inclination of the straight line perpendicular to the straight line sqrt3x+y=1 .

Prove that "The greatest chord of circle is its diameter".

The equation of straight line passing through the origin and making an angle alpha with the straight line x+y=0 is

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

Find the equation of the straight line which passes through the centre of the circle x^(2) + y^(2) + 2x + 2y- 23 = 0 and is perpendicular to the straight line x-y+8 = 0.

Two circles intersect each other at the points P and Q. A straight line passing through P intersects one circle at A the other circle at .A straight line passing through Q intersect the first circle at C and the second circle at D. Prove that AC||BD .