Circles And Construction

       
           

Points to Remember:-
a) Equal chords of a circle (or of congruent circles) subtend equal angles at the centre.
b) If two chords of a circle subtend equal angles at the centre, then the chords are equal.
c) The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
d) The perpendicular from the centre of a circle to a chord bisects the chord.
e) Equal chords of a circle are equidistant from the centre whereas the equidistant chords from the centre are equal.
f) Chords corresponding to equal arcs are equal.
g) Congruent arcs of a circle subtend equal angles at the centre.
h) The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part.
i) Angles in the same segment are equal, whereas the angle in a semicircle is a right angle.
j) The sum of either pair of opposite angles of a cyclic Quadrilateral is 1800.
k) If the opposite angles of a Quadrilateral are supplementary, then the quadrilateral is cyclic.
l) If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, then the four points are cyclic.

Topics Covered in Circles And Construction

Circles and Its Related Terms

The locus of a point which moves in a plane in such a manner that its distance from a given fixed point is always constant, is called a circle.
The fixed point is called the centre and constant distance is call...Read More

Math Topics