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Symmetry Properties of a Circle

Symmetry Properties of a Circle. A. O. B. 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?. Symmetry Properties of the chords of a circle.

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Symmetry Properties of a Circle

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  1. Symmetry Properties of a Circle

  2. A O B 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?

  3. 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

  4. 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

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

  6. 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

  7. 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

  8. Time to Work • Ex 11A Page 77 • Q 1 to 3

  9. line D line C line B line E line A 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.

  10. O A B C 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. • OB is the radius. • ABC is the tangent.

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

  12. A B O j C 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

  13. Time to Work • Home work • Skill Practice 11B Page 81 • Q1b, c • Q2a, b • Q3a, b • Q4 • Q6 • Class Work • Skill Practice 11B Page 81 • Q1a,d • Q2c,d • Q3c,d • Q5 • Q7 • Q8

  14. 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.

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