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## CIRCLE

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**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**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**Diameter and radi**AOB is called diameter O A B AO is called radii**Chord and apothem**OB is called Apothem O ABC is called Chord A C B**Sector and segment**The shaded area is called Segment The shaded area is called Sector**Arc, segment and sector**Minor sector Mayor arc Mayor Segment Minor segment Minor arc Mayor sector**The formula to find circumference and the area of circle**Circumference: 2 x x r or πd Area: x r²**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**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**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**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**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**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= 2r = 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.**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 = 2r = 2 x 3.14 x (6,400 + 1,600) = 50,240 km**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**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**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**Created By:**Windy Lestari 8D