Difference between revisions of "The longest chord passes through the centre of the circle"

Latest revision as of 16:17, 4 November 2019

Investigating the diameter is the longest chord of a circle.

Objectives

To understand longest chord passes through the centre and it is the diameter

Estimated Time

30 minutes

Prerequisites/Instructions, prior preparations, if any

Prior knowledge of point, lines, angles, polygons

Materials/ Resources needed

Digital : Computer, geogebra application, projector.
Non digital : Worksheet and pencil, compass, strings
Geogebra files : Diameter is longest chord.ggb

Download this geogebra file from this link.

Process (How to do the activity)

Use the geogebra file to show how diameter is the longest chord.

Move the points on the circle to show the changes in the triangle.

What is the condition with respect to sides for formation of a triangle. Sum of two sides is larger than the third side.

Compare the chord length with sum of two radii. When is the triangle reduced to a line segment.

What can you conclude about the chord? When is it the largest?

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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>
+===Objectives===
+To understand longest chord passes through the centre and it is the diameter
+===Estimated Time===
+minutes
-<!-- This portal was created using subst:box portal skeleton  -->
+===Prerequisites/Instructions, prior preparations, if any===
-<!--        BANNER ACROSS TOP OF PAGE        -->
+Prior knowledge of point, lines, angles, polygons
-{| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;"
-|-
-|style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
-[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
-|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
-|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
-[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
-|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
-[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
-|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
-[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]
-|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
-[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
-|}
-While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
-= 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}}
-= 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
-=Additional Information=
+Move the points on the circle to show the changes in the triangle.
-==Useful websites==
-#[http://www.regentsprep.org/Regents/math/geometry/GP14/PracCircleSegments.htm www.regentsprep.com] conatins good objective problems on chords and secants <br>
-#[http://www.mathwarehouse.com/geometry/circle/tangents-secants-arcs-angles.php www.mathwarehouse.com] contains good content on circles for different classes<br>
-#[http://staff.argyll.epsb.ca/jreed/math20p/circles/tangent.htm staff.argyll]  contains good simulations
-==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.
-= 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
-==Concept #1 Chord==
-===Learning objectives===
-# Meaning of circle and chord.
-# Method to measure the perpendicular distance of the chord from the centre of the circle.
-# Properties of chord.
-# Able to relate chord properties to find unknown measures in a circle.
-# Apply chord properties for proof of further theorems in circles.
-# Understand the meaning of congruent chords.
-===Notes for teachers===
-# A chord is a straight line joining 2 points on the circumference of a circle.
-# Chords within a circle can be related in many ways.
-# The theorems that involve chords of a circle are :
-* Perpendicular bisector of a chord passes through the center of a circle.
-* Congruent chords are equidistant from the center 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 they determine two central angles that are congruent.
-===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]]
-#Activity No 2 - [[Circles_and_lines_activity_2|Theorem 2.Congruent chords are equidistant from the center of a circle]]
-==Concept #2.Secant and Tangent==
+[[Category:Circles]]
-===Learning objectives===
-# The secant is a line passing through a circle touching it at any two points on the circumference.
-# A tangent is a line toucing the circle at only one point on the circumference.
-===Notes for teachers===
-===Activities===
-#Activity #1 - [[Circles_and_lines_activity_3|Understanding secant and tangent using Geogebra]]
-==Concept #3 Construction of tangents==
-===Learning objectives===
-# The students should know that tangent is a straight line touching the circle at one and only point.
-# They should understand that a tangent is perpendicular to the radius of the circle.
-# The construction protocol of a tangent.
-# Constructing a tangent to a point on the circle.
-# Constructing tangents to a circle from external point at a given distance.
-# A tangent that is common to two circles is called a common tangent.
-# A common tangent with both centres on the same side of the tangent is called a direct common tangent.
-# A common tangent with both centres on either side of the tangent is called a transverse common tangent.
-===Notes for teachers===
-===Activities===
-#Activity #1 - [[Circles_and_lines_activity_4|Construction of Direct common tangent]]
-#Activity #2 - [[Circles_and_lines_activity_5|Construction of Transverse common tangent]]
-==Concept #4 Cyclic quadrilateral==
-===Learning objectives===
-# A quadrilateral ABCD is called cyclic if all four vertices of it lie on a circle.
-# In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.
-# If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.
-# In a cyclic quadrilateral the exterior angle is equal to interior opposite angle
-===Notes for teachers===
-===Activities===
-#Activity #1 - [[Circles_and_lines_activity_6|Cyclic quadrilateral]]
-#Activity #2 - [[Circles_and_lines_activity_7|Properties of cyclic quadrilateral]]
-= Hints for difficult problems =
-#Tangents AP and AQ are drawn to circle with centre O, from an external point A. Prove that  ∠PAQ=2.∠ OPQ
-Please click [http://karnatakaeducation.org.in/KOER/en/index.php/Class10_circles_tangents#Problem_1 here] for solution.
-[[Class10_circles_tangents|here]]
-= Project Ideas =
-= Math Fun =
-'''Usage'''
-Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template