Circles

Circles explained with definitions, radius–diameter relationships, chords, arcs, tangents, theorems, and easy-to-follow examples.

1.Definition of a Circle and Basic Terms
Understand what a circle is and learn the basic terms like centre, radius, diameter, chord, arc, sector and segment with simple student-friendly notes.
2.Radius of a Circle
Understand the meaning of radius, how it defines a circle, its relation with diameter, and how radii behave in different constructions.
3.Diameter of a Circle
Learn what the diameter of a circle is, how it relates to the radius, and why it is the longest chord in a circle.
4.Chords of a Circle
Learn what chords are, how they behave inside a circle, and the important properties connecting chords, radius, perpendicular bisectors, and the centre of the circle.
5.Arcs of a Circle
Understand what arcs are, how they are formed in a circle, and the difference between minor arcs, major arcs, and semicircles.
6.Sectors of Circle
Learn what sectors are, the difference between minor and major sectors, and how to calculate the area of a sector in a circle.
7.Concentric Circles
Learn what concentric circles are, how they share the same centre, and where they appear in daily life and geometric constructions.
8.Congruent Circles
Learn what congruent circles are and how equality of radii determines whether two circles are congruent.
9.Central Angles
Learn what central angles are, how they relate to arcs, and the key properties connecting central angles, chords, and arc measures in a circle.
10.Inscribed Angles (Angles in the Same Segment)
Learn what inscribed angles are, how they relate to arcs and central angles, and the important theorem about angles in the same segment of a circle.
11.Cyclic Quadrilaterals
Learn what cyclic quadrilaterals are, their defining properties, angle relations, and the important theorems used in circle geometry.
12.Tangents to a Circle
Learn what tangents are, how they touch the circle at exactly one point, and the geometric properties of tangents drawn from a point.
13.Properties of Tangents from an External Point
Learn the key properties of tangents drawn from an external point to a circle, including equal tangents theorem, angle relations, and geometric reasoning.
14.Secants of a Circle
Understand what secants are in a circle, how they intersect the circle at two points, and how secants relate to chords and tangents.
15.Perpendicular Bisector Theorem of a Chord
Learn the perpendicular bisector property of a chord and how the radius from the centre bisects the chord at 90 degrees.
16.Equal Chords Theorem
Understand the equal chords theorem and how equal chords in a circle correspond to equal arcs and equal distances from the centre.
17.Equal Arcs Theorem
Learn how equal arcs in a circle relate to equal chords and equal central angles, with clear geometric reasoning.
18.Chord–Distance from Centre Relationship
Learn how the distance of a chord from the centre of a circle determines its length, and why chords closer to the centre are longer.
19.Chord Length and Central Angle Theorem
Learn how the length of a chord is related to the central angle it subtends, along with formulas and intuitive understanding.
20.Power of a Point
Understand the Power of a Point theorem, including secant–secant, tangent–secant, and chord–chord cases with clear student-friendly explanations.
21.Circumference of a Circle
Learn what the circumference of a circle is, how to calculate it using radius or diameter, and understand the role of π in the formula.
22.Area of a Circle
Learn what the area of a circle means, how to calculate it using radius or diameter, and why the formula involves π.
23.Area of a Sector
Learn how to find the area of a sector of a circle using the central angle, radius, and the formula involving π.
24.Area of a Segment
Learn how to find the area of a segment of a circle using the central angle, radius, and the difference between sector area and triangle area.