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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''']. − + − __FORCETOC__+ − <mm>[[circles_and_lines.mm|flash]]</mm>+ + + − + − To add textbook links, please follow these instructions to: + − ([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage]) − =Additional Information=+ − ==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==+ − = Teaching Outlines =+ − 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===+ − #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==+ − ===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
The longest chord passes through the centre of the circle (view source)
Revision as of 16:17, 4 November 2019
, 16:17, 4 November 2019added Category:Circles using HotCat
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
= Concept Map =
===Materials/ Resources needed===
* Digital : Computer, geogebra application, projector.
* 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)===
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?
[[Category:Circles]]