Symmetry Properties of a Circle

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Presentation transcript:

Symmetry Properties of a Circle

Chords A and B are any two points on the circumference of the circle , center O. The line segment AB is called a chord. What is the longest chord of a circle? O B A

Symmetry Properties of the chords of a circle The line through the midpoint of a chord of a circle and the centre of the circle is perpendicular to the chord. If AC = BC then OCA =OCB = 90

Symmetry Properties of the chords of a circle The perpendicular from the centre of a circle to a chord of the circle bisects the chord. If OCB = 90, then AC = BC

Symmetry Properties of the chords of a circle OA = OB OAC =OBC OAB is an isosceles triangle Note : AOC =BOC as OAC  OBC

Symmetry Properties of the chords of a circle Equal chords of a circle are equidistant from the centre of the circle. If AB = CD, then OE = OF

Symmetry Properties of the chords of a circle Chords of a circle which are equidistant from the centre of the circle are equal in length. If OE = OF, then AB = CD

Time to Work Ex 11A Page 77 Q 1 to 3

Tangent A tangent is a line that intersects the circle at exactly one point and is perpendicular to a radius at that point of intersection. line A line D line C line B line E

Symmetry Properties of the Tangents to a circle A tangent to a circle is perpendicular to the radius of the circle at the point of contact. O B A C OB is the radius. ABC is the tangent.

Symmetry Properties of the Tangents to a circle Tangents drawn from an external point to a circle are equal in length. j B O C A OA = OC (radius) AB and BC are the tangents Hence AB = CB

Symmetry Properties of the Tangents to a circle The angle between the tangents drawn from an external point to a circle is bisected by the line through the external point of the centre of the circle. Given AB and CB are the tangents, then OAB = OCB = 90 OBA = OBC AOB = COB j B O C A

Time to Work Class Work Skill Practice 11B Page 81 Q1a,d Q2c,d Q3c,d Home work Skill Practice 11B Page 81 Q1b, c Q2a, b Q3a, b Q4 Q6

Property 1: A circle is symmetrical about every diameter. Hence any chord AB perpendicular to a diameter is bisected by the diameter. Also, any chord bisected by a diameter is perpendicular to the diameter.