G E O M E T R Y

1. GEOMETRY Circle Terminology

2. Component of Geometry • Point (dot) • Line At least two points given • Angle  If two line intersect in a point • Plane  Something which has area • Space  something which boundary at least by two plane

3. Circle • Set of points which have same distance into one permanent point Same distance = radius = r Permanent point is central point

4. The segment joining the center of a circle to a point on the circle. Example: OA Radius (or Radii for plural) adopted from http://www.worldofteaching.com

5. A chord that passes through the center of a circle. Example: AB What is AO? What is OB? What is relation between radius and diameter? Diameter Radius Radius d=2r

6. A segment joining two points on a circle Example: AB Chord

7. A segment joining two points on a circle Example: AB AB= diameter So, what is relation between chord and diameter? Chord Diameter is the longest chord

8. A line that intersects the circle at exactly two points. Example: AB Secant

9. A line that intersects the circle at exactly two points. Example:AB Secant

10. A line that intersects a circle at exactly one point. Example: AB Tangent

11. An angle whose vertex is at the center of a circle. Example: Angle ABC Central Angle

12. An angle whose vertex is on a circle and whose sides are determined by two chords. Example: Angle ABC Inscribed Angle

13. A figure consisting of two points on a circle and all the points on the circle needed to connect them by a single path. Example: arc AB Arc What is the longest arc? circumference

14. An arc that lies in the interior of an inscribed angle. Example: arc AC Intercepted Arc

15. If angle is inside the circle. Example: arc AC arc DF Two Intercepted Arc

16. If angle is outside the circle. Example: arc DE arc DC Two Intercepted Arc

17. Apothem • The shortest distance between center point and chord • Example: OA A

18. O Segment • Area which bordered by arc and chord • Shaded area is minor segment • Plain area is major segment

19. O Sector • Area which bordered by two radii and an arc • Shaded area is minor sector • Plain area is major sector

20. Tangents of the circle

21. Requirements:- • Compass • Pencils • Eraser • Scale • Set Square

22. Tangent Chord Secent • If line touches the circle at one point only that is called a tangent • If line connect the two point at the circle that is called a chord • If line intersect the circle at two point that is called secant

23. Circle Chord Formation of tangent D P Tangent C Secant A B

24. Defination of tangents APB is called a tangentto the circle The touching point P is called the point of contact. A P C B

25. When two circles do not touch A B E H P Q G F C D We construct four tangentsAB,CD, EF & GH

26. When two circles touches externally 3rd Tangent 1st Tangent A P • B . . R O O’ C Q 2nd Tangent D We can construct three tangents APB, CQD, PRQ

27. When two circles intersect each other 1st Tangent A B . . O ! O C 2nd Tangent D We can construct two tangents AB, CD

28. When two circles touches internally A P O O’ B We can construct onlyone tangents APB

29. When two concurrent circles O’ O We can not construct any common tangent

30. Pis a point out side the circle you canconstruct twotangents passing throughP Q P O R Tangent PQ = TangentPR

31. Constructing Circumcircle Steps of Construction C Construct a Δ ABC Bisect the side AB Bisect the side BC o The two lines meet at O From O Join B B Taking OB as radius draw a circumcircle. A

32. Bisect the BAC Bisect the ABC Taking O draw OP AB Constructing of incircle C Steps ofconstruction Construct a Δ ABC O The two lines meet at O Taking OP as radius Draw a circumcircle A B P