If two intersecting chords of a circle produce equal angles with the straight line obtained by joining the point of intersection and the centre, then prove that the chords are equal.

If two intersecting chords of a circle make equal angles with diameter passing through their point of intersection, prove that the chords are equal.

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

Two parallel straight lines are drawn through the points of intersection of two circles upto their circumference. Then prove that two straight lines are equal.

Prove analytically that the straight line joining the middle point of a chord of a circle with the centre is perpendicular to the chord.

Prove that the internal angle between two tangents drawn from an external point is bisected by the straight line obtained by joining that point and the centre of the circle.

The equation of the locus of the middle point of a chord of the circle x^2+y^2=2(x+y) such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally inclined to the x-axis is (a) x+y=2 (b) x-y=2 (c) 2x-y=1 (d) none of these

If two tangents are drawn to a circle from a point outside it, then the line segment joining the point of contact and the exterior point are equal and they subtend equal angles at the centre.

If the straight line intersects the circle at two points, then the straight line is called a "_____" to the circle.

Prove that if two tangents are drawn to a circle from a point outside it, then the line segments joining the point of contacts and the exterior point are equal.

Prove that if two tangents are drawn to a circle from a point outside it, then the line segments joining the point of contact and the exterior point are equal and they subtend equal angles at the centre.