Circles

While creating a resource page, please click here for a resource creation checklist.

= Concept Map = Flash

= Textbook =

ncert books
Class 9 Mathematics contain simple description and theorems on circles. 9 Mathematics contain higher level description and theorems on circles.

=Additional Information=

Useful websites

 * 1) maths is fun A GOOD WEBSITE ON DEFINITIONS FOR CIRCLES
 * 2) COOL MATH GIVES CLEAR AND EASY DEFINITIONS
 * 3) OPEN REFERENCE CONTAINS FEW SIMULATIONS
 * 4) WIKIPEDIA CONTAINS EXPLANATIONS FOR CIRCLES
 * 5) KHAN ACADEMY CONTAIN GOOD VIDEOS
 * 6) ARVIND GUPTA TOYS CONTAIN VERY GOOD BOOKS ON MATHEMATICS AND SCIENCE
 * 7) nrich.maths.org Contain very good description of Pie

Reference Books

 * 1) School Geometry By Hall and Stevens. Part3 pageno 143. Contains basic definitions and proofs given by Euclid.

= Teaching Outlines = Introduction

The following is a background literature for teachers. It summarises the things to be known for a teacher to teach this topic more effectively. This literature is meant to be a ready reference for the teacher to develop the concepts, inculcate necessary skills and impart knowledge in Geometry - Circles from Class 6 to Class 10.

The first step is to understand how to define circles and related terms using geometric vocabulary. The next step is to understand what is Pi. That it is a constant and that for any circle the ratio of the circumference by the diameter is always a constant value Pi. The interesting properties of Pi – an irrational number can also be discussed here in the basic form. Ability for the child to do simple area and perimeter calculations. Next the learner should understand that the circle is a 2 dimensional plane figure and how to visualise solid 3-dimensional figures. What are the solid shapes that have a circle as a part of them. Mensuration – more complex area measurements which include circular shapes. Surface Area and Volume measurement of sold shapes such as cylinder, sphere and cone. Understand the properties of the circles by proving theorems deductively. Also acquire the skills of deductive proofs, understand that all the properties can be deduced from the axioms. Understand the relationship between lines and circles – secant and tangent

Notes for teachers
Definition:A circle is a collection of all points in a plane, which are equidistant from a fixed point.

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #
<ggb_applet width="761" height="554" version="4.0" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="false" />
 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets


 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources


 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #
<ggb_applet width="625" height="564" version="4.2" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="false" />
 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

= Hints for difficult problems =

= Project Ideas =

= Math Fun =

Usage

Create a new page and type to use this template