Circumference of a Circles REVIEW

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

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

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

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

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

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

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

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

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 = 69.08 cm R 11 cm

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=?

AREA of a Circles

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

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

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

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

Area of 14 pieces = area of the //gram = bh = r( r) = r² 6 14 2 4 8 10 12 h= r r 11 3 9 13 1 5 7 base = C or b= r

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 = 379.94 cm² R 11 cm

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 = 50.24 cm² R 4 cm

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 = 153.86 cm²

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

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

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

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

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

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

AREAS OF REGULAR POLYGONS

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

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)

NAME THE PARTS CENTRAL ANGLE THE CENTER THE RADIUS 2 1 ANGLE 1 AND ANGLE 2

NAME THE PARTS APOTHEM

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.

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

FIND THE AREA OF A REGULAR HEXAGONS WITH A 9 cm APOTHEM. SOLUTION: Use 30-60-90 ∆ ½s = = 3 Multiply both sides by 2 S= 6 9 CM 60 ½ s So, perimeter is equals to 36

FIND THE AREA OF A REGULAR HEXAGONS WITH A 9 cm APOTHEM. SOLUTION: A = ½ap = ½( 9cm)36 cm = ½( 324 cm² ) = 162 cm² 9 CM 60 ½ s So, perimeter is equals to 36

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