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Chapter 11 of 18
Concept Maps

The Circle — Concept Maps

ICSE · Class 11 · Mathematics

4 concept maps of The Circle for ICSE Class 11 Mathematics, each also written out as a text outline. Part of the ICSE Class 11 Mathematics syllabus.

72 questions28 flashcards20 formulas & key relations5 concepts

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A labeled diagram illustrating the definition of a circle with its center and radius.
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4 Concept Maps

Circle Equations and Properties Overview

Circle Equations and Properties Overview

The map in words

  • Circle
    • Definition
      • Locus of points
      • Equidistant from center
      • Fixed distance radius
    • Equations
      • Standard Form
        • Center h k
        • Radius r
        • Formula derived
      • General Form
        • Expanded version
        • Coefficients g f c
        • Center and radius
      • Diameter Form
        • Endpoints given
        • Perpendicular property
        • Direct equation
      • Parametric Form
        • Angle parameter
        • Trigonometric functions
        • Circular motion
    • Properties
      • Center point
      • Radius length
      • Diameter longest chord
      • Circumference formula
    • Applications
      • Engineering design
      • Computer graphics
      • Physics motion
      • Real world problems

Circle Concepts Overview

Circle Concepts Overview

The map in words

  • Circle
    • Definitions
      • Center
      • Radius
      • Chord
      • Diameter
    • Equations
      • Standard Form
        • Center Radius Given
        • Point on Circle Given
      • General Form
        • Completing Square
        • Three Points Given
      • Diameter Form
        • Angle in Semicircle
      • Parametric Form
        • Applications
    • Properties
      • Position of Points
        • Inside
        • On Circle
        • Outside
      • Two Circles
        • External Tangent
        • Internal Tangent
        • Intersecting
        • Separate
        • One Inside Other

Circle Equations Overview

Circle Equations Overview

The map in words

  • Circle Equations
    • Standard Form
      • Center-Radius
      • （x-h）² + （y-k）² = r²
      • Most Direct
    • General Form
      • Expanded
      • x² + y² + 2gx + 2fy + c = 0
      • -g,-f
      • Radius √(g²+f²-c)
    • Diameter Form
      • Endpoints Given
      • （x-x₁）（x-x₂） + （y-y₁）（y-y₂） = 0
      • Right Angle Property
    • Parametric Form
      • x = h + r cos θ
      • y = k + r sin θ
      • Motion Based

Circle as the locus of points in a plane equidistant from a fixed point

Circle as the locus of points in a plane equidistant from a fixed point

The map in words

  • Circle as the locus of points in a plane equidistant from a fixed point
    • Definition of Circle
    • Basic Terms
    • Standard Equation
    • General Equation
    • Diameter Equation
    • Parametric Equation
    • Position of a Point and a Circle
    • Relative Position of Two Circles

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Frequently Asked Questions

What are the important topics in The Circle for ICSE Class 11 Mathematics?
Key topics in The Circle include Basic ideas and terms, Standard equation of a circle, General equation of a circle, Diameter equation of a circle. Study these first, then practise questions on each for Class 11 exams.
What do the concept maps for The Circle show?
The 4 maps show how the ideas in The Circle connect: Circle Equations and Properties Overview; Circle Concepts Overview. Each map is also written out as an outline on this page.
How should I revise The Circle for Class 11 exams?
Learn the core ideas first, then work through the 72 practice questions on The Circle. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for The Circle

All ICSE Class 11 Mathematics Concept Maps

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