In this chapter, we will learn

The basics - What is a circle, radius, diameter, arc, sector, segment, chord

Then, we do some theorems, and related questions... like

Equal chords subtends equal angle at the center, and its converse

Perpendicular from center to a chord bisects the chord, and its converse

Only 1 Circle can pass through 3 non-collinear points

Equal chords subtend equal angles at the center, and its converse

Angle subtended by an arc is double the angle subteneded at any other point

Angles in the same segment of a circle are equal

Then, we will learn what a Cyclic Quadrilateral is,

And its property - Sum of opposite angles of cyclic quadrilateral is 180.

1. Circle: The collection of all points in a plane which are at a fixed distance from a fixed point in the plane is called a circle.

2. Basic Definition

Chord: Suppose, we take any two points on a circle, then the line segment PQ is called the chord of the circle.

Diameter: The chord which passes through the centre of the circle is called a diameter AB of the circle.

Arc: A piece of a circle between two points is called an arc. If P and Q are any two points on them, the PQ is an arc of the circle and it is denoted by AB.

Circumference: The length of the complete circle is called its circumference.

Semi-circle: A diameter of a circle divides it into two equal parts which an arc. Each of these two arcs is called a semi-circle.

Congruent Circles (Arc): Two circles are said to be congruent if and only if either of them can be superposed on the other so as to cover exactly.

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

Common Chord: The intersection point of two circles is the common chord of the circle.