1. WELCOME

2. Teacher Introduction Md. Shamsuzzaman Lecturer(Mathematics) Joypurhat Girls' Cadet College

3. Subject: Mathematics Class: Eight Time: 40 min Date: 09-09-2015

4. Ring Football Wheel Watch

5. Todays Lesson Circle

6. Objectives: 1. To define a circle. 2. To know centre, radius, diameter, chord, arc and circumference of the circle. 3. To proof circle related theorem.

7. Circle: A circle is the locus of all points equidistant from a central point. O is the center and OA be the radius of the circle. Radius: Distance from center of circle to any point on it. OA Diameter: The longest distance from one end of a circle to the other. Chord: A line segment within a circle that touches two points on the circle. Arc: A curved line that is part of the circumference of a circle. Circumference: The distance around the circle. Pi(π): A number, 3.141592......equal to (the circumference) ⁄ (the diameter) of any circle. O AB

8. Single Work: Draw a circle and show centre, radius, diameter and chord of the circle.

9. Solution: A O D C B In the circle, O is the centre, OA=OB=radius, AB=diameter and CD=Arc of the circle.

10. Theorem 1: The line segment joining the center of a circle to midpoint of a chord other than diameter, is perpendicular to the chord. A B O M Proposition: Let AB be a chord other than diameter of a circle with centre O and O is joined to the midpoint M of AB. Let us prove that OM is the perpendicular to AB. Construction: Join O, A and O, B.

11. A B O M Proof: Steps Justification M is the midpoint of AB Radius of the same circle common side SSS Theorem

12. Group Work: Prove that the perpendicular from the centre of a circle to a chord bisects the chord.

13. A B O M Proposition: Let AB be a chord other than diameter of a circle with centre O and OM is the perpendicular to AB. Let us prove that, OM bisects the chord AB. Construction: Join O, A and O, B. Solution:

14. A B O M Proof: Steps Justification Radius of the same circle common side SSS Theorem 1.Since OM is perpendicular to AB. <OMA=<OMB=1 right angle. 2. Now, in right angle triangle OMA and OMB hypotenuse OA=hypotenuse OB OM=OM Triangle OMA and OMB are congruent. Therefore. AM=BM. i,e OM bisects the chord AB.

15. Evaluation: 1. Which is the greatest chord of the circle? 2.What is the relation between radius and diameter?

16. Solution: 1.Diameter. 2.Radius is half of the diameter. Or, Diameter is double of the radius.

17. Home Work: 1. Draw a circle with 3 cm radius and prove that diameter is equal to twice the radius.

18. Thanks