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| + | Investigating the diameter is the longest chord of a circle. |
− | ''[http://karnatakaeducation.org.in/KOER/index.php/೧೦ನೇ_ತರಗತಿಯ_ವೃತ್ತ_-_ಸ್ಪರ್ಶಕದ_ಗುಣಲಕ್ಷಣಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div>
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| + | ===Objectives=== |
| + | To understand longest chord passes through the centre and it is the diameter |
| + | ===Estimated Time=== |
| + | 30 minutes |
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| + | ===Prerequisites/Instructions, prior preparations, if any=== |
− | <!-- BANNER ACROSS TOP OF PAGE -->
| + | Prior knowledge of point, lines, angles, polygons |
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− | [http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
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− | [http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
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− | [http://karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
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− | [http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
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− | = Concept Map = | + | ===Materials/ Resources needed=== |
− | __FORCETOC__
| + | * Digital : Computer, geogebra application, projector. |
− | <mm>[[circles_and_lines.mm|flash]]</mm>
| + | * Non digital : Worksheet and pencil, compass, strings |
| + | * Geogebra files : [https://ggbm.at/c4eg7q2u Diameter is longest chord.ggb] |
| + | {{Geogebra|c4eg7q2u}} |
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− | = Textbook = | + | ===Process (How to do the activity)=== |
− | To add textbook links, please follow these instructions to:
| + | Use the geogebra file to show how diameter is the longest chord. |
− | ([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage]) | |
− | #[http://ktbs.kar.nic.in/New/Textbooks/class-x/english/maths/class-x-english-maths-chapter14.pdf Karnataka text book for Class 10, Chapter 14 - Chord properties]
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− | #[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]
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| | | |
− | =Additional Information=
| + | Move the points on the circle to show the changes in the triangle. |
− | ==Useful websites==
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− | #[http://www.regentsprep.org/Regents/math/geometry/GP14/PracCircleSegments.htm www.regentsprep.com] conatins good objective problems on chords and secants <br>
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− | #[http://www.mathwarehouse.com/geometry/circle/tangents-secants-arcs-angles.php www.mathwarehouse.com] contains good content on circles for different classes<br>
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− | #[http://staff.argyll.epsb.ca/jreed/math20p/circles/tangent.htm staff.argyll] contains good simulations
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− | ==Reference Books==
| + | What is the condition with respect to sides for formation of a triangle. Sum of two sides is larger than the third side. |
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− | = Teaching Outlines =
| + | Compare the chord length with sum of two radii. When is the triangle reduced to a line segment. |
− | Chord and its related theorems
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− | ==Concept #1 Chord==
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− | ===Learning objectives===
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− | # Meaning of circle and chord.
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− | # Method to measure the perpendicular distance of the chord from the centre of the circle.
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− | # Properties of chord.
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− | # Able to relate chord properties to find unknown measures in a circle.
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− | # Apply chord properties for proof of further theorems in circles.
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− | # Understand the meaning of congruent chords.
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− | ===Notes for teachers===
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− | # A chord is a straight line joining 2 points on the circumference of a circle.
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− | # Chords within a circle can be related in many ways.
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− | # The theorems that involve chords of a circle are :
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− | * Perpendicular bisector of a chord passes through the center of a circle.
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− | * Congruent chords are equidistant from the center of a circle.
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− | * If two chords in a circle are congruent, then their intercepted arcs are congruent.
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− | * If two chords in a circle are congruent, then they determine two central angles that are congruent.
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| | | |
− | ===Activities===
| + | What can you conclude about the chord? When is it the largest? |
− | #Activity No 1 - [[Circles_and_lines_activity_1|Theorem 1: Perpendicular bisector of a chord passes through the center of a circle]]
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− | #Activity No 2 - [[Circles_and_lines_activity_2|Theorem 2.Congruent chords are equidistant from the center of a circle]]
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| | | |
− | ==Concept #2.Secant and Tangent==
| + | [[Category:Circles]] |
− | ===Learning objectives===
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− | # The secant is a line passing through a circle touching it at any two points on the circumference.
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− | # A tangent is a line toucing the circle at only one point on the circumference.
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− | ===Notes for teachers===
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− | ===Activities===
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− | #Activity #1 - [[Circles_and_lines_activity_3|Understanding secant and tangent using Geogebra]]
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− | | |
− | ==Concept #3 Construction of tangents==
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− | ===Learning objectives===
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− | # The students should know that tangent is a straight line touching the circle at one and only point.
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− | # They should understand that a tangent is perpendicular to the radius of the circle.
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− | # The construction protocol of a tangent.
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− | # Constructing a tangent to a point on the circle.
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− | # Constructing tangents to a circle from external point at a given distance.
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− | # A tangent that is common to two circles is called a common tangent.
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− | # A common tangent with both centres on the same side of the tangent is called a direct common tangent.
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− | # A common tangent with both centres on either side of the tangent is called a transverse common tangent.
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− | | |
− | ===Notes for teachers===
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− | ===Activities===
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− | #Activity #1 - [[Circles_and_lines_activity_4|Construction of Direct common tangent]]
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− | #Activity #2 - [[Circles_and_lines_activity_5|Construction of Transverse common tangent]]
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− | | |
− | ==Concept #4 Cyclic quadrilateral==
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− | ===Learning objectives===
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− | # A quadrilateral ABCD is called cyclic if all four vertices of it lie on a circle.
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− | # In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.
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− | # If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.
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− | # In a cyclic quadrilateral the exterior angle is equal to interior opposite angle
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− | ===Notes for teachers===
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− | ===Activities===
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− | #Activity #1 - [[Circles_and_lines_activity_6|Cyclic quadrilateral]]
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− | #Activity #2 - [[Circles_and_lines_activity_7|Properties of cyclic quadrilateral]]
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− | | |
− | = Hints for difficult problems =
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− | #Tangents AP and AQ are drawn to circle with centre O, from an external point A. Prove that ∠PAQ=2.∠ OPQ
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− | Please click [http://karnatakaeducation.org.in/KOER/en/index.php/Class10_circles_tangents#Problem_1 here] for solution.
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− | | |
− | [[Class10_circles_tangents|here]]
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− | = Project Ideas =
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− | = Math Fun =
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