The line joining the centre of a circle to the mid-point of a chord is perpendicular to the chord.

Fill in the Blanks: The line drawn through the centre of a circle to ______ a chord is perpendicular to the chord.

The perpendicular from the centre of a circle to a chord bisects the chord.

(True/ False) Line segment joining the centre to any point on the circle is a radius of the circle.

If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chord.

Find the locus of the middle points of equal chords of a circle.

The length of a chord of a circle is 4 cm. If its perpendicular distance from the centre is 1.5 cm, determine the radius of the circle.

If four points be taken on a rectangular hyperbola such that the chord joining any two is perpendicular to the chord joining the other two, and if alpha,beta,gamma,delta be the inclinations to either asymptotes of the straight lines joining these points to the centre, then tanalphatanbetatangammatandelta is equal to