Changes

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

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

== Additional Resources[edit | edit source] ==

== Additional Resources[edit | edit source] ==

=== OER[edit | edit source] ===

=== OER[edit | edit source] ===

#*This is a video showing construction of tangent at any point on a circle

#*This is a video showing construction of tangent at any point on a circle

{{#widget:YouTube|id=LLKFqv71i0s|left}} : This is a resource file created by Suchetha, Mathematics teacher, GJC Thyamangondlu

{{#widget:YouTube|id=LLKFqv71i0s|left}}  

#*This is a video showing construction of tangent from external point and theorem  

 

{{#widget:YouTube|id=xvXaxx1u-iA|left}} : This is a resource file created by Suchetha, Mathematics teacher, GJC Thyamangondl

This is a resource file created by Suchetha, Mathematics teacher, GJC Thyamangondlu

*** you want see the kannada videos on theorems and construction of circle [http://karnatakaeducation.org.in/KOER/index.php/%E0%B3%A7%E0%B3%A6%E0%B2%A8%E0%B3%87_%E0%B2%A4%E0%B2%B0%E0%B2%97%E0%B2%A4%E0%B2%BF%E0%B2%AF_%E0%B2%B5%E0%B3%83%E0%B2%A4%E0%B3%8D%E0%B2%A4_-_%E0%B2%B8%E0%B3%8D%E0%B2%AA%E0%B2%B0%E0%B3%8D%E0%B2%B6%E0%B2%95%E0%B2%A6_%E0%B2%97%E0%B3%81%E0%B2%A3%E0%B2%B2%E0%B2%95%E0%B3%8D%E0%B2%B7%E0%B2%A3%E0%B2%97%E0%B2%B3%E0%B3%81 click here] this is shared by Yakub koyyur GHS Nada.

*This is a video showing construction of tangent from external point and theorem  

{{#widget:YouTube|id=xvXaxx1u-iA|left}}  

 

This is a resource file created by Suchetha, Mathematics teacher, GJC Thyamangondl

 

*This is a video showing Transverse common tangent

 

 

 

** you want see the kannada videos on theorems and construction of circle [http://karnatakaeducation.org.in/KOER/index.php/%E0%B3%A7%E0%B3%A6%E0%B2%A8%E0%B3%87_%E0%B2%A4%E0%B2%B0%E0%B2%97%E0%B2%A4%E0%B2%BF%E0%B2%AF_%E0%B2%B5%E0%B3%83%E0%B2%A4%E0%B3%8D%E0%B2%A4_-_%E0%B2%B8%E0%B3%8D%E0%B2%AA%E0%B2%B0%E0%B3%8D%E0%B2%B6%E0%B2%95%E0%B2%A6_%E0%B2%97%E0%B3%81%E0%B2%A3%E0%B2%B2%E0%B2%95%E0%B3%8D%E0%B2%B7%E0%B2%A3%E0%B2%97%E0%B2%B3%E0%B3%81 click here] this is shared by Yakub koyyur GHS Nada.

# Books and journals

# Books and journals

# Textbooks

# Textbooks

##[http://ktbs.kar.nic.in/New/Textbooks/class-x/english/maths/class-x-english-maths-chapter15.pdf Karnataka text book for Class 10, Chapter 15 - Tangent Properties]

##[http://ktbs.kar.nic.in/New/Textbooks/class-x/english/maths/class-x-english-maths-chapter15.pdf Karnataka text book for Class 10, Chapter 15 - Tangent Properties]

# Syllabus documents (CBSE, ICSE, IGCSE etc)

# Syllabus documents (CBSE, ICSE, IGCSE etc)

== Learning Objectives ==

== Learning Objectives ==

* Appreciation of circle as an important shape as it is an intrical component in the invention of almost everything that we see around us.

* Appreciation of circle as an important shape as it is an intrical component in the invention of almost everything that we see around us.

====== [[Introduction to chords]] ======

====== [[Introduction to chords]] ======

A chord is the interval joining two distinct points on a circle. This activity investigates formation of chord and compares with the diameter of the circle.

A chord is the interval joining two distinct points on a circle. This activity investigates formation of chord and compares with the diameter of the circle.

====== [[Secant and tangent of a circle]] ======

====== [[Secant and tangent of a circle]] ======

The theorems that involve chords of a circle are :

The theorems that involve chords of a circle are :

* Perpendicular bisector of a chord passes through the center of a circle.

* Perpendicular bisector of a chord passes through the centre of a circle.

* Congruent chords are equidistant from the center of a circle.

* Congruent chords are equidistant from the centre of a circle.

* If two chords in a circle are congruent, then their intercepted arcs are congruent.

* If two chords in a circle are congruent, then their intercepted arcs are congruent.

* If two chords in a circle are congruent, then they determine two central angles that are congruent.   

* If two chords in a circle are congruent, then they determine two central angles that are congruent.   

====== [[Chord length and distance for centre of the circle]] ======

====== [[Chord length and distance for centre of the circle]] ======

For a chord the distance from the center is the   perpendicular distance of the chord such that it passes through the center.

For a chord the distance from the centre is the perpendicular distance of the chord such that it passes through the centre.

====== [[The longest chord passes through the centre of the circle]] ======

====== [[The longest chord passes through the centre of the circle]] ======

Investigating the diameter is the longest chord of a circle.

Investigating the diameter is the longest chord of a circle.

====== [[Perpendicular bisector of a chord passes through the center of a circle]] ======

====== [[Perpendicular bisector of a chord passes through the center of a circle|Perpendicular bisector of a chord passes through the centre of a circle]] ======

Since every perpendicular bisector passes through the centre, the centre must lie on every one of them, so the centre must be their single common point.

Since every perpendicular bisector passes through the centre, the centre must lie on every one of them, so the centre must be their single common point.

====== [[Congruent chords are equidistant from the centre of a circle|Congruent chords are equidistant from the center of a circle]] ======

 

====== [[Congruent chords are equidistant from the centre of a circle|Congruent chords are equidistant from the centre of a circle]] ======

In the same circle or in circles of equal radius:

In the same circle or in circles of equal radius:

*Use the fact that a tangent line and the radius through that point of tangency are perpendicular to solve for a third value. Show how you can also use this fact to deduce whether or not a line is tangent to a specific circle.

*Use the fact that a tangent line and the radius through that point of tangency are perpendicular to solve for a third value. Show how you can also use this fact to deduce whether or not a line is tangent to a specific circle.

*Tangents from an external point are equal in length.

*Tangents from an external point are equal in length.

==Types of tangents==

==Types of tangents==

*Recognise the difference between a secant and a tangent of a circle.

*Recognise the difference between a secant and a tangent of a circle.

==== '''Construction of tangents''' ====

==== '''Construction of tangents''' ====

*[[Image:KOER%20Circles_html_50027288.png|link=https://karnatakaeducation.org.in/KOER/en/index.php/File:KOER_Circles_html_50027288.png]]

*[[Image:KOER%20Circles_html_50027288.png|link=]]

*<u>To draw a tangent to a circle from an external point </u>  [[Image:KOER%20Circles_html_m520802ec.png|link=https://karnatakaeducation.org.in/KOER/en/index.php/File:KOER_Circles_html_m520802ec.png]]

*<u>To draw a tangent to a circle from an external point </u>  [[Image:KOER%20Circles_html_m520802ec.png|link=]]

*<u>To draw direct common tangents to two given circles of equal radii, with centres ‘d’ units apart. </u>  [[Image:KOER%20Circles_html_4b7743eb.png|link=https://karnatakaeducation.org.in/KOER/en/index.php/File:KOER_Circles_html_4b7743eb.png]]

*<u>To draw direct common tangents to two given circles of equal radii, with centres ‘d’ units apart. </u>  [[Image:KOER%20Circles_html_4b7743eb.png|link=]]

*<u>To draw a direct common tangent to two circles of different radii. </u>  [[Image:KOER%20Circles_html_3b9c6f9.png|link=https://karnatakaeducation.org.in/KOER/en/index.php/File:KOER_Circles_html_3b9c6f9.png]]To construct Transverse common tangents to two circles.

*<u>To draw a direct common tangent to two circles of different radii. </u>  [[Image:KOER%20Circles_html_3b9c6f9.png|link=]]

==== [[Circles Tangents Problems]] ====

 

To construct Transverse common tangents to two circles.

To construct Transverse common tangents to two circles.

[[Image:KOER%20Circles_html_m38f1dae5.png|link=]]

[[Image:KOER%20Circles_html_m38f1dae5.png|link=]]

====Learning Objectives====

====Learning Objectives====

Acquire knowledge about the

Acquire knowledge about the

====Pre-requisites/Instructions====

====Pre-requisites/Instructions====

Please refer to the document 22-Tangents  [[:File:2.7 Circles - Tangent Activities.pdf]]  and complete the exercises.

Please refer to the document 22-Tangents  [[:File:2.7 Circles - Tangent Activities.pdf]]  and complete the exercises.

======  [[Construction of direct common tangent]] ======

======  [[Construction of direct common tangent]] ======

The direct common tangents to two circles meet on the line of centres and divide it externally in the ratio of the radii. 

The direct common tangents to two circles meet on the line of centres and divide it externally in the ratio of the radii. 

====== [[Construction of transverse common tangent]] ======

====== [[Construction of transverse common tangent]] ======

The transverse common tangents also meet on the line of centres and divide it internally in the ratio of the radii.

The transverse common tangents also meet on the line of centres and divide it internally in the ratio of the radii.

===Projects (can include math lab/ science lab/ language lab) ===

===Projects (can include math lab/ science lab/ language lab) ===

#Collect different types of circular objects

#Collect different types of circular objects