Circles

The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a .

The fixed point is called the of the circle

The fixed distance is called the of the circle.

The line segment joining the centre and any point on the circle is also called a of the circle.

The chord, which passes through the centre of the circle, is called a of the circle.

The length of the complete circle is called its .

The region between a chord and either of its arcs is called a of the circular region.

The region between an arc and the two radii, joining the centre to the end points of the arc is called a .

When two arcs are equal, that is, each is a semicircle, then both segments and both sectors become the same and each is known as a .

Equal chords of a circle subtend at the centre.

If the angles subtended by the of a circle at the centre are equal, then the chords are equal.

The line drawn through the centre of a circle to bisect a chord is to the chord.

There is one and only passing through three given non-collinear points.

Chords equidistant from the centre of a circle are equal in .

If two chords of a circle are equal, then their corresponding arcs are and .

If two arcs are congruent, then their corresponding chords are .

The angle subtended by an arc at the centre is the angle subtended by it at any point on the remaining part of the circle.

Angles in the same of a circle are equal.

A quadrilateral ABCD is called if all the four vertices of it lie on a circle .

The sum of either pair of opposite angles of a cyclic quadrilateral is º

If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is .

Angle in a semicircle is a .

Circles

Gap-fill exercise