Difference between revisions of "The longest chord passes through the centre of the circle"
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===Notes for teachers=== | ===Notes for teachers=== | ||
===Activities=== | ===Activities=== | ||
− | #Activity #1 - Construction of Direct common tangent | + | #Activity #1 - [[Circles_and_lines_activity_4|Construction of Direct common tangent]] |
− | #Activity #2 - Construction of Transverse common tangent | + | #Activity #2 - [[Circles_and_lines_activity_5|Construction of Transverse common tangent]] |
==Concept #4 Cyclic quadrilateral== | ==Concept #4 Cyclic quadrilateral== | ||
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===Activities=== | ===Activities=== | ||
#Activity #1 - [[Circles_and_lines_activity_6|Cyclic quadrilateral]] | #Activity #1 - [[Circles_and_lines_activity_6|Cyclic quadrilateral]] | ||
+ | #Activity #2 - [[Circles_and_lines_activity_7|Properties of cyclic quadrilateral]] | ||
+ | |||
= Hints for difficult problems = | = Hints for difficult problems = |
Revision as of 21:17, 9 July 2014
Philosophy of Mathematics |
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Concept Map
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Textbook
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Additional Information
Useful websites
- www.regentsprep.com conatins good objective problems on chords and secants
- www.mathwarehouse.com contains good content on circles for different classes
- 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 - Theorem 1: Perpendicular bisector of a chord passes through the center of a circle
- Activity No 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 - 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 - Construction of Direct common tangent
- Activity #2 - 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 - Cyclic quadrilateral
- Activity #2 - 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 here for solution.
Project Ideas
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