The longest chord passes through the centre of the circle

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= Concept Map =

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=Additional Information=

Useful websites

 * 1) www.regentsprep.com conatins good objective problems on chords and secants
 * 2) www.mathwarehouse.com contains good content on circles for different classes
 * 3) staff.argyll contains good simulations

Reference Books
= Teaching Outlines = Chord and its related theorems

Learning objectives

 * 1) Meaning of circle and chord.
 * 2) Method to measure the perpendicular distance of the chord from the centre of the circle.
 * 3) Properties of chord.
 * 4) Able to relate chord properties to find unknown measures in a circle.
 * 5) Apply chord properties for proof of further theorems in circles.
 * 6) Understand the meaning of congruent chords.

Notes for teachers

 * 1) A chord is a straight line joining 2 points on the circumference of a circle.
 * 2) Chords within a circle can be related in many ways.
 * 3) 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

 * 1) Activity No 1 - Theorem 1: Perpendicular bisector of a chord passes through the center of a circle
 * 2) Activity No 2 - Theorem 2.Congruent chords are equidistant from the center of a circle

Learning objectives

 * 1) The secant is a line passing through a circle touching it at any two points on the circumference.
 * 2) A tangent is a line toucing the circle at only one point on the circumference.

Activities

 * 1) Activity #1 - Understanding secant and tangent using Geogebra

Learning objectives

 * 1) The students should know that tangent is a straight line touching the circle at one and only point.
 * 2) They should understand that a tangent is perpendicular to the radius of the circle.
 * 3) The construction protocol of a tangent.
 * 4) Constructing a tangent to a point on the circle.
 * 5) Constructing tangents to a circle from external point at a given distance.
 * 6) A tangent that is common to two circles is called a common tangent.
 * 7) A common tangent with both centres on the same side of the tangent is called a direct common tangent.
 * 8) A common tangent with both centres on either side of the tangent is called a transverse common tangent.

Activities

 * 1) Activity #1 - Construction of Direct common tangent
 * 2) Activity #2 - Construction of Transverse common tangent

Learning objectives

 * 1) A quadrilateral ABCD is called cyclic if all four vertices of it lie on a circle.
 * 2) In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.
 * 3) If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.
 * 4) In a cyclic quadrilateral the exterior angle is equal to interior opposite angle

Activities

 * 1) Activity #1 - Cyclic quadrilateral
 * 2) Activity #2 - Properties of cyclic quadrilateral

= Hints for difficult problems = Please click here for solution.
 * 1) Tangents AP and AQ are drawn to circle with centre O, from an external point A. Prove that ∠PAQ=2.∠ OPQ

here

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