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CIRCLE

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  1. C Ircle Contents 3.The formula to find circumference and the area of a circle 1.Definition circle 2.Part of circle 4.The relation ship between a central angle, an arc’s length and a sector’s area 5.Constructing The in circle of triangle and circum circle of triangle 6.The circle’s circumference and area in application

  2. DefinitionCircle Circle is a curved line that tip and base line meet and every point on the curved line has same distance to one point

  3. Parts of circle

  4. Diameter and radi AOB is called diameter O A B AO is called radii

  5. Chord and apothem OB is called Apothem O ABC is called Chord A C B

  6. Sector and segment The shaded area is called Segment The shaded area is called Sector

  7. Arc, segment and sector Minor sector Mayor arc Mayor Segment Minor segment Minor arc Mayor sector

  8. The formula to find circumference and the area of circle Circumference: 2 x  x r or πd Area:  x r²

  9. Exercise 1 • Find circumference and the area of the circle that have following radii: - 7 cm - 70 cm - 42cm - 54 cm 2. 35cm Find the area and the perimeter of the figures in the left

  10. The relation ship between a central angle, an arc’s length and a sector’s area To the circle shown in figure 1 the following relation apply: Measure of AOB angle = length of arc … = area of… 360° … … or Area of sector OAB = AOB angle x … 360° Length of arc AB = AOB angle x … 360° B O A

  11. Exercise 2 B 1. In the circle shown Ab is 12.56 cm the area of the sector OAB is 2. In the circle bellow the area of the sector OPQ is 18.84 cm² and the measure of POQ angle is 60° Find the length of radius OP A 40° O P Q O

  12. Constructing The incircle of a triangle • Construct ABC triangle then construct the bisector of BAC angle • 2. Construct the bisector of ABC angle such that it coincides with the bisector • 3. Construct a line PQ which is perpendicular to the line AB with the point Q lying on the line AB C • 4. Construct a circle centered at P with PQ as its radius P A Q B

  13. Constructing the circumference of a triangle 1. Construct ABC triangle, and then construct the bisector 2. Construct the perpendicular bisector of QR such that it intersect that of PQ at point O 3. Join the point O to point Q R 4. Construct a circle centered at O with OQ as its radius the completed circle is the circumcircle of PQR triangle P Q

  14. The circle’s circumference and area in application

  15. Example : A wheel has a radius of 25 cm. What is the distance the wheel. Travels if it rotates through 100 Full turns? Answer: Radius = 25 cm or r =25 K= 2r = 2 x 3.14 x 25 = 157 The distance travelled after rotating through 100 full turns: 100 x 157 = 1,5700 cm = 157 m Remember: If the wheel rotates through one full turns then it travels a distance equal to its circumference.

  16. An artificial satellite is in an orbit 1,600 km Above earth’s surface. The radius of the earth is 6,400 km, and the satellite’s orbit is Assumed to be circular. If it takes the The satellite 8 hours to complete one orbit, Then find the circumference of its orbit Answer: Orbit circumference = outer circle’s circumference = 2r = 2 x 3.14 x (6,400 + 1,600) = 50,240 km

  17. Exercise 3 • A bicycle wheel rotates through 900 full turns to travel a distance of 847.8 m. Find the circumference and the radius of the wheel • An artificial satellite is in an orbit 900 km above earth’s surface. The radius of the earth is 6,400 km, and the satellite’s orbit is assumed to be circular • A wheel has a radius of 24 cm. Find the distance the wheel travels after rotating through full truns

  18. Competency about circle 1. In the semi circle shown the area of the shaded region is … 2. In the circle shown AOB triangle is 72 degree and OA is 21 cm the area of the sector OAB is 8 cm 12 cm B A O

  19. 3. A wheel rotating through 2,000 full turns travels a distance of 5, 204m. Find the area of each wheel’s circular face is …….. 4. The area of a circle that having a perimeter of 37.68 cm is ……… 5. In the above figure PQ is 16 cm and QR is 12 cm. Find the area of the shaded region below 6. A minute hand of a clock is 20 cm long. If the hand rotates for 25 minutes, then the distance the tip of the hand travels is……. S R O Q P

  20. Created By: Windy Lestari 8D