1. Symmetry Properties of a Circle

2. 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

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. 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

10. 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.

11. 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

12. 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

13. 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

16. 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.