1. Circumference of a Circles
REVIEW

2. NAME MY PARTS
Tangent
– Line which intersects the circle at exactly one point.
Point of Tangency
– the point where the tangent line and the circle intersect (C) L D
Secant – Line which intersects the circle at exactly two points.
e.g. DL C M

3. NAME EACH OF THE FOLLOWING:
1. A Circle C B D
Answer Circle O O A E

4. NAME EACH OF THE FOLLOWING:
2. All radii C B D
Answer AO, BO, CO DO, EO O A E

5. NAME EACH OF THE FOLLOWING:
3. All Diameters C B D
Answer AD and BE, O A E

6. NAME EACH OF THE FOLLOWING:
4. A secant C B D
Answer BC O A E k

7. NAME EACH OF THE FOLLOWING:
5. A Tangent C B D
Answer EK O A E k

8. NAME EACH OF THE FOLLOWING:
5. Point of Tangency C B D
Answer E O A E k

9. CIRCUMFERENCE Circumference – is a distance around a circle.
Circumference of a Circle is determined by the length of a radius and the value of pi.
The formula is
C= 2r or C = d r P

10. WHAT IS THE CIRCUMFERENCE OF A CIRCLE IF RADIUS IS 11 cm?
EXAMPLE 1
WHAT IS THE CIRCUMFERENCE OF A CIRCLE IF RADIUS IS 11 cm?
Solution:
C = 2r
C = 2( 11 cm)
C = 22cm or
C = cm R
11 cm

11. THE CIRCUMFERENCE OF A CIRCLE IS 14cm. HOW LONG IS THE RADIUS?
EXAMPLE 2
THE CIRCUMFERENCE OF A CIRCLE IS 14cm. HOW LONG IS THE RADIUS?
Solution:
C = 2r
14cm = 2r
Dividing both sides by 2 .
7 cm = r or
r = 7 cm R
r=?

13. AREA of a Circles

14. IS IT POSSIBLE TO COMPLETELY FILLED THE CIRCLE WITH A SQUARE REGIONS?
INVESTIGATION
IS IT POSSIBLE TO COMPLETELY FILLED THE CIRCLE WITH A SQUARE REGIONS?
NO. R

15. HOW IS THE AREA OF THE CIRCLE MEASURED?
INVESTIGATION
HOW IS THE AREA OF THE CIRCLE MEASURED?
In terms of its RADIUS. R

16. WHAT IS THE NEW FIGURE FORMED?
INVESTIGATION
TAKE A CIRCULAR PIECE OF PAPER CUT INTO 16 EQUAL PIECES AND REARRANGE THESE PIECES
WHAT IS THE NEW FIGURE FORMED? r

17. NOTICE THAT THE NEW FIGURE FORMED RESEMBLES A PARALLELOGRAM.
The BASE is approximately equal to half the circumference of the circular region. 6 14 2 4 8 10 12
h= r r 11 3 9 13 1 5 7
base = C or b= r

18. Area of 14 pieces = area of the //gram = bh = r( r) = r²6 14 2 4 8 10 12
h= r r 11 3 9 13 1 5 7
base = C or b= r

19. WHAT IS THE AREA OF A CIRCLE IF radius IS 11 cm?
EXAMPLE 1
WHAT IS THE AREA OF A CIRCLE IF radius IS 11 cm?
Solution:
A = r ²
= ( 11 cm)²
A = 121cm² or
= cm² R
11 cm

20. WHAT IS THE AREA OF A CIRCLE IF radius IS 4 cm?
EXAMPLE 2
WHAT IS THE AREA OF A CIRCLE IF radius IS 4 cm?
Solution:
A = r ²
= ( 4 cm)²
A = 16cm² or
= cm² R
4 cm

21. EXAMPLE 3 Solution: Step 1. find r. Step 2. find the area C = 2r
THE CIRCUMFERENCE OF A CIRCLE IS 14cm. WHAT IS THE AREA OF THE CIRCLE?
Solution:
Step 1. find r.
C = 2r
14cm = 2r
Dividing both sides by 2 .
7 cm = r or
r = 7 cm
Step 2. find the area
A = r ²
= ( 7 cm)²
A = 49cm² or
= cm²

22. EXAMPLE 4 Solution: Step 1. find r. Step 2. find the area C = 2r
THE CIRCUMFERENCE OF A CIRCLE IS 10cm. WHAT IS THE AREA OF THE CIRCLE?
Solution:
Step 1. find r.
C = 2r
10cm = 2r
Dividing both sides by 2 .
5 cm = r or
r = 5 cm
Step 2. find the area
A = r ²
= ( 5 cm)²
A = 25cm² or
= 78.5 cm²

23. 1. All radii of a circle are congruent.
TRUE OR FALSE
1. All radii of a circle are congruent.
ANSWER
TRUE

24. 2. All radii have the same measure.
TRUE OR FALSE
2. All radii have the same measure.
ANSWER
FALSE

25. 3. A secant contains a chord.
TRUE OR FALSE
3. A secant contains a chord.
ANSWER
TRUE

26. 4. A chord is not a diameter.
TRUE OR FALSE
4. A chord is not a diameter.
ANSWER
TRUE

27. TRUE OR FALSE
5. A diameter is a chord.
ANSWER
TRUE

28. AREAS OF REGULAR POLYGONS

29. REGULAR POLYGONS 6 SIDES 3 SIDES 4 SIDES 5 SIDES 7 SIDES 8 SIDES

30. The radius of a regular polygon is the distance from the center to the vertex.
Given any circle, you can inscribed in it a regular polygon of any number of sides.
The central angle of a regular polygon is an angle formed by two radii.
It is also true that if you are given any regular polygon, you can circumscribe a circle about it.
The center of a regular polygon is the center of the circumscribed circle.
This relationship between circles and regular polygons leads us to the following definitions.
The apothem of a regular polygon is the (perpendicular) distance from the center of the polygon to a side. 2 1
APOTHEM( a)

31. NAME THE PARTS CENTRAL ANGLE THE CENTER THE RADIUS2 1
ANGLE 1 AND ANGLE 2

32. NAME THE PARTS
APOTHEM

33. AREAS OF REGULAR POLYGONS
The area of a regular polygon is equal to HALF the product of the APOTHEM and the PERIMETER.
AREAS OF REGULAR POLYGONS
A = ½ap where, a is the apothem and p is the perimeter of a regular polygon.

34. FIND THE AREA OF A REGULAR HEXAGONS WITH A 9 cm APOTHEM.
REMEMBER: Each vertex angle regular hexagon is equal to 120°. each vertex  = S ÷ n
HINT: A radius of a regular hexagon bisects the vertex angle.
9 CM

35. FIND THE AREA OF A REGULAR HEXAGONS WITH A 9 cm APOTHEM.
SOLUTION: Use ∆ ½s = = 3 Multiply both sides by 2 S= 6
9 CM 60
½ s
So, perimeter is equals to 36

36. FIND THE AREA OF A REGULAR HEXAGONS WITH A 9 cm APOTHEM.
SOLUTION: A = ½ap = ½( 9cm)36 cm = ½( cm² ) = cm²
9 CM 60
½ s
So, perimeter is equals to 36

37. FIND THE AREA OF A REGULAR triangle with radius 4
4 CM 60
½ s