Yaadannoo boqonnaa fi gaaffii shaakalaa

Boqonnaa 5 Herrega kutaa 10: Geengoo

Wanti fuula kana irra jiru hundi boqonnaa 5 kitaaba Herrega kutaa 10 tiif: wanta boqonnaan haguugu, yaadannoo gabaabaa, gaaffii shaakalaa deebii isaanii waliin, fi viidiyoo barnootaa bakka jirutti.

5
Kaardii: 10
Gaaffii shaakalaa boqonnaa 5: 237–270
Fuula kitaabaa boqonnaa 5

Boqonnaan 5 maal haguuga

1.Symmetrical properties of circles
2.Angle properties of circles
3.Theorems on angles and arcs determined by lines

Yaadannoo gabaabaa boqonnaa 5

Kaardiiwwan fuula Herrega kutaa 10 irratti boqonnaa kana jala galmaa'an. Tokko tokkoon bani.

Kofa Kordiiwwan Keessatti WalqaxxaamuraniiFoormulaa

\theta = \frac{1}{2}(\alpha + \beta)

\theta = \frac{1}{2}(\alpha + \beta)

$\theta$: Kofa keessoo shoordota wal qaxxaamuran gidduu jiru $deg$
$\alpha$: Safara aarkii kofamee tokkoffaa $deg$
$\beta$: Safara aarkii kofamee lammaffaa $deg$

Yoom akka itti fayyadamtu

Kordiiwwan lama keessoo geengoo keessatti yoo walqaxxaamuran kofa uumamu arkiilee qabaman irraa shallaguuf fayyadami.

Of eeggadhu

Gatii arkiilee lamaanii walitti dabali malee walirraa hin hir'isin.

Grade 10 Mathematics, fuula 238-271 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Dheerina ArkiiFoormulaa

s = \frac{\theta}{360^{\circ}} \cdot 2\pi r

s = \frac{\theta}{360^{\circ}} \cdot 2\pi r

$s$: Dheerina aarkii $m$
$\theta$: Kofa gidduugaleessaa $deg$
$r$: Raadiyeesii $m$
$\pi$: Dhaabbataa paayii $unitless$

Yoom akka itti fayyadamtu

Dheerina arki geengoo shallaguuf yeroo raadiyasiin fi kofli gidduugaleessaa beekamanitti fayyadami.

Of eeggadhu

Kofli kenname kofa gidduugaleessaa digriidhaan ta'uu isaa mirkaneeffadhu.

Grade 10 Mathematics, fuula 238-271 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Balina SekteraaFoormulaa

A = \frac{\theta}{360^{\circ}} \pi r^2

A = \frac{\theta}{360^{\circ}} \pi r^2

$A$: Baldhina seektaraa $m^2$
$\theta$: Kofa gidduugaleessaa $deg$
$r$: Raadiyeesii $m$
$\pi$: Dhaabbataa paayii $unitless$

Yoom akka itti fayyadamtu

Balina sekterii geengoo kan raadiyasiilee lamaafi arkiin daangeffame shallaguuf fayyadami.

Of eeggadhu

Raadiyasiin r qofti iskuweerii ta'a, pi waliin erga baay'ateen booda miti.

Grade 10 Mathematics, fuula 238-271 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Dheerina KordiiFoormulaa

c = 2r \sin\left(\frac{\theta}{2}\right)

c = 2r \sin\left(\frac{\theta}{2}\right)

$c$: Dheerina shoordii $m$
$r$: Raadiyeesii $m$
$\theta$: Kofa gidduugaleessaa shoordiin uumame $deg$

Yoom akka itti fayyadamtu

Dheerina kordii kofa gidduugaleessaan uumame shallaguuf qoverride kana fayyadami.

Of eeggadhu

Saayinii shallaguun dura kofa theta bakka lamatti qoodi.

Grade 10 Mathematics, fuula 238-271 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Dogoggora Pirimtiree SekteraaDogoggora baratame

Yoom akka itti fayyadamtu

Pirimtiree sekteraa shallaguun yeroo gaafatamu yaadannoo kana fayyadami.

Of eeggadhu

Dheerina arki qofa shallaguun dogoggora. Pirimtireen sekteraa raadiyasiilee lamaan dabalachuu qaba, P = s + 2r.

Grade 10 Mathematics, fuula 238-271 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Gaaffii shaakalaa boqonnaa 5

Gaaffii filannoo 10 boqonnaa kana irratti barreeffaman, tokkoon tokkoon isaanii deebii fi sababa qabu. Deebii banuu dura yaali. Gaaffiin kun Ingiliffaa tiin.

Gaaffii 1

A circle is the set of points in a plane that are all the same distance from one fixed point. What is this fixed point called?

A.chord
B.center
C.diameter
D.tangent

Deebii fi sababa agarsiisi

Deebii: B center

Sababa

The fixed point is called the center of the circle. The constant distance from the center is the radius.

Gaaffii 2

How many lines of symmetry does a circle have?

A.0
B.1
C.4
D.infinite

Deebii fi sababa agarsiisi

Deebii: D infinite

Sababa

A circle has infinite lines of symmetry. Any diameter of a circle is a line of symmetry, and a circle has infinitely many diameters.

Gaaffii 3

A circular plot of teff in Bahir Dar has radius 7 m. Using π = 22/7, what is the perimeter of the plot?

A.22 m
B.44 m
C.154 m
D.308 m

Deebii fi sababa agarsiisi

Deebii: B 44 m

Sababa

The perimeter of a circle is P = 2πr.

P = 2 × (22/7) × 7 = 44 m.

Gaaffii 4

A line is drawn from the center O of a circle, perpendicular to a chord AB. The line meets AB at N. What does this line do to the chord AB?

A.It cuts AB into two equal parts, so AN = NB.
B.It makes AB equal to the radius.
C.It makes AB longer than the diameter.
D.It makes AB a tangent to the circle.

Deebii fi sababa agarsiisi

Deebii: A It cuts AB into two equal parts, so AN = NB.

Sababa

Theorem 5.2 says that a line drawn from the center perpendicular to a chord bisects the chord. This means it cuts the chord into two equal parts, so AN = NB.

Gaaffii 5

In a circle, an inscribed angle and a central angle both cover the same arc. The inscribed angle is 35°. What is the central angle?

A.17.5°
B.35°
C.70°
D.145°

Deebii fi sababa agarsiisi

Deebii: C 70°

Sababa

Theorem 5.6 says the inscribed angle is half of the central angle. So the central angle is twice the inscribed angle.

Central angle = 2 × 35° = 70°.

Gaaffii 6

A chord AB of a circle with radius 10 cm is 16 cm long. What is the distance from the center of the circle to the chord?

A.6 cm
B.8 cm
C.10 cm
D.12 cm

Deebii fi sababa agarsiisi

Deebii: A 6 cm

Sababa

The perpendicular from the center cuts the chord in half, so MB = 8 cm. Use the right triangle OMB, where OB is the radius.

OM = √(OB² − MB²) = √(10² − 8²) = √(100 − 64) = √36 = 6 cm.

Gaaffii 7

A sector of a circular garden in Addis Ababa has radius 6 m and a central angle of 210°. Using π = 22/7, what is the area of the sector?

A.33 m2
B.66 m2
C.132 m2
D.198 m2

Deebii fi sababa agarsiisi

Deebii: B 66 m2

Sababa

The area of a sector is A = πr² × (θ/360°).

A = (22/7) × 6² × (210/360) = (22/7) × 36 × (7/12) = 66 m².

Gaaffii 8

AB is the diameter of a circle. C is another point on the circle, so triangle ABC is formed. Angle ABC = 55°. What is angle BAC?

A.125°
B.90°
C.35°
D.55°

Deebii fi sababa agarsiisi

Deebii: C 35°

Sababa

An angle in a semicircle is a right angle (Thales' Theorem). So angle ACB = 90°.

The angles of a triangle add up to 180°, so angle BAC = 180° − 90° − 55° = 35°.

Gaaffii 9

The four angles of a cyclic quadrilateral are (4y + 2)°, (y + 20)°, (5y − 2)° and 7y°. What is the value of y?

A.18
B.20
C.22
D.24

Deebii fi sababa agarsiisi

Deebii: B 20

Sababa

The four angles of a cyclic quadrilateral add up to 360°.

(4y + 2) + (y + 20) + (5y − 2) + 7y = 360
17y + 20 = 360
17y = 340
y = 20.

Gaaffii 10

A chord of a circle with radius 6 cm subtends a central angle of 120°. What is the length of the chord?

A.6 cm
B.6√3 cm
C.12 cm
D.12√3 cm

Deebii fi sababa agarsiisi

Deebii: B 6√3 cm

Sababa

The chord length is 2r sin(θ/2).

Chord = 2 × 6 × sin(60°) = 12 × (√3/2) = 6√3 cm.

Appiin boqonnaa kana irratti gaaffii 12 qaba; utuu hojjettuu ni sirreessa. Kan asii jiran 10 jalqabaa ti.

Fuula kitaabaa boqonnaa 5

Boqonnaan 5 Maxxansa Ministeera Barnootaa keessatti fuula 237 hanga fuula 270 ti.

Maxxansa Ministeera Barnootaa, Ingiliffaa, Fuula 373

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Yaadannoo gabaabaa Herrega kutaa 10 hunda

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