creation of polygons by using arc,general methods

Exterior Angle method
Construct a hexagon length of side 30 mm

Construct a pentagon of length of side 30 mm

1. Exterior Angle method Construct a hexagon length of side 30 mm Take 360/6=60

2. 60 60 120

3. 60 60 120

4. 60 60 120 F E D C 30

5. Construct a pentagon of length of side 30 mm Take 360/5=72 A B

6. Take 360/5=72 A B

7. Take 360/5=72 A B 30 72 72 C D E

8. Construct An Octagon given the length of side 30mm Take 360/8=45 A B

9. A B Take 360/8=45 45 45

10. A B Take 360/8=45 45 45

11. A B Take 360/8=45 45 45

12. A B Take 360/8=45 45 45 H G F E d c 25

13. A B Take 360/8=45 45 45 H G F E d c 25

14. CONSTRUCTION OF REGULAR HEXAGON Construct a regular hexagon of side 30 mm when one side is a.Horizontal b.One side is vertical

15. o

16. o A

17. o A A as the center given side length as radius cut B on the circle B C D E F

18. o A A as the center given side length as radius cut B on the circle B C D E F

19. CONSTRUCTION OF REGULAR HEXAGON Construct a regular hexagon of side 30 mm when one side is a.Horizontal b.One side is vertical

20. o A

21. o A as the center given side length as radius cut B on the circle A B C D E F

22. o A as the center given side length as radius cut B on the circle A B C D E F

23. WHEN ONE SIDE IS HORIZONTAL A B 30

24. WHEN ONE SIDE IS HORIZONTAL A B 30

25. WHEN ONE SIDE IS HORIZONTAL A B 30 O TAKE OA AS RADIUS DRAW THE CIRCLE

26. WHEN ONE SIDE IS HORIZONTAL A B 30 O TAKE OA AS RADIUS DRAW THE CIRCLE C C D

27. WHEN ONE SIDE IS HORIZONTAL A B 30 O TAKE OA AS RADIUS DRAW THE CIRCLE C C D

28. WHEN IT IS VERTICAL

29. Inscription of polygons Inscribe a regular polygon of sides say 5 in a circle of 60 mm diameter when one side is horizontal

30. o R=30mm

31. o R=30mm Number of sides N=5 360/5=72

32. o R=30mm Number of sides N=5 360/5=72 If We Want To Draw One Side Of The Pentagon To Be Horizontal Draw A Vertical Radial Line Op

33. o R=30mm Number of sides N=5 360/5=72 P

34. o R=30mm Number of sides N=5 360/5=72 P 36 36

35. o R=30mm Number of sides N=5 360/5=72 P 36 36 A B

36. o R=30mm Number of sides N=5 360/5=72 P 36 36 A B E D C 72

37. o R=30mm Number of sides N=5 360/5=72 P 36 36 A B E D C 72 60 Above method is common for the inscription of all polygons

38. Inscribe a hexagon in a circle of 70 mm diameter Inscribe a regular polygon of any number of sides say 5 in a given circle of 70 mm diameter

39. O 70MM

40. O P M

41. O P M DIVIDE THE PM INTO 5 EQUAL PARTS 1 2 3 4

42. O P M DIVIDE THE PM INTO 5 EQUAL PARTS 1 2 3 4 P and M as centers and PM as radius ,draw arcs cutting each other at R R

43. O P M DIVIDE THE PM INTO 5 EQUAL PARTS 1 2 3 4 R JOIN R2 Join R2 and extend it up to Q

44. O P M DIVIDE THE PM INTO 5 EQUAL PARTS 1 2 3 4 R Join R2 and extend it up to Q Q

45. O P M DIVIDE THE PM INTO 5 EQUAL PARTS 1 2 3 4 R Join R2 and extend it up to Q Q PQ AS THE RADIUS CUT THE CIRCLE

46. O P M DIVIDE THE PM INTO 5 EQUAL PARTS 1 2 3 4 R Join R2 and extend it up to Q Q PQ AS THE RADIUS CUT THE CIRCLE R S T THIS METHOD IS COMMON FOR THE INSCRIPTION OF ALL POLYGONS

47. INSCRIPTION OF PENTAGON INSCRIBE A REGULAR HEXAGON IN A GIVEN CIRCLE OF 70 MM DIAMETER WHEN TWO SIDES OF THE HEXAGON ARE A . HORIZONTAL B. VERTICAL

48. 70MM R=35

49. 70MM R=35 WITH R=35 MM RADIUS SET OF THE CIRCLE

50. 70MM R=35 WITH R=35 MM RADIUS SET OF THE CIRCLE A B C D E F

51. INSCRIPTION OF OCTAGON 70 MM DIA 35MM

52. INSCRIPTION OF OCTAGON 70 MM DIA 35MM A B C D

53. INSCRIPTION OF OCTAGON 70 MM DIA 35MM A B C D

54. INSCRIPTION OF OCTAGON 70 MM DIA 35MM A B C D E F G H

55. INSCRIPTION OF OCTAGON 70 MM DIA 35MM A B C D E F G H 70

56. SUPERSCRIPTION /CIRCUMSRIPTION OF POLYGONS DESCRIPE AN EQUILATERAL TRIANGLE ABOUT A CIRCLE OF 50 MM DIA METER

57. 25MM

58. 360/3=120 O A B C

59. 360/3=120 O A B C 120 120