latihan soal lingkaran
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Latihan Soal LingkaranTRANSCRIPT
![Page 1: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/1.jpg)
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Soal - 1
O
D
C
A
B
400
600
Pada gambar di samping, panjang usur AB = 30 cm, AOB = 400, dan COD = 600.
Hitunglah panjang busur CD.
![Page 3: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/3.jpg)
PembahasanDiketahui :
AB = 30 cm, AOB = 400, dan COD = 600
Besar AOB=
Pjg. busur AB
Besar CODPjg. busur
CD40
0 =
30 cm
600 X cm
X = ( 30 x 60 ) : 40 = 45 cm.
![Page 4: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/4.jpg)
Soal - 2
O
A
B600
Pada gambar disamping, panjang jari-jari = 21 cm, AOB = 600.
Hitunglah:
a.L.juring OAB
b. Pj. Busur AB
![Page 5: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/5.jpg)
Diketahui :
AOB = 600, dan jari-jari = 21 cm
Besar AOB=
L. Juring OAB
3600 L. Lingkaran
600
=x
3600 r2
X = ( 22 x 63 ) : 6 = 1231 cm2.
Jadi L. Juring OAB = 231 cm2.
1=
x
6 22/7 x 21 X
21
Pembahasan :
![Page 6: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/6.jpg)
Diketahui :
AOB = 600, dan jari-jari = 21 cm
Besar AOB
=
Pj. Busur AB
3600
K. Lingkaran
600
=x
3600 2r
X = 132 : 6 = 22 cm.
Jadi Pj. Busur AB = 22 cm.
1=
x
62 x 22/7 x
21
![Page 7: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/7.jpg)
Soal - 3
Panjang jari-jari sebuah roda
21 cm. Berapakah panjang
lintasannya jika roda itu
berputar atau menggelinding
sebanyak 600 kali.
![Page 8: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/8.jpg)
Diketahui :Panjang jari-jari = 21 cmJumlah putaran = 600 kali
Keliling roda = 2 r = 2 x 22/7 x 21
= 2 x 66 = 132 cm.Panjang lintasannya = 600 x 132 cm = 79.200 cm = 792 meter.
Pembahasan :
![Page 9: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/9.jpg)
Soal - 4
Sebuah roda berputar sebanyak 200 kali untuk melintasi jalan sepanjang 314 meter.
Hitunglah :
a.Keliling roda
b.Jari-jari roda
![Page 10: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/10.jpg)
Diketahui :Panjang lintasan = 314 meterJumlah putaran = 200 kali
Keliling roda = Pjg. lintasan : jlh putaran = (314 x 100 )cm : 200 = 157 cm.Jari-jari roda = Keliling : 2 = 157 : 2 x 3,14 = 157 : 6,28 = 25 cm.
Pembahasan :
![Page 11: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/11.jpg)
Soal - 5
42 cm
Hitunglah luas daerah yang diarsir !
![Page 12: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/12.jpg)
Pembahasan :
Luas lingkaran yang diarsir :L = ½ r2 = ½ x 22/7 x 21 x 21 = ½ x 22 x 63 = 11 x 63 = 693 cm2
42 cm
Lingkaran kecil diarsir = lingkaran kecil tdk diarsir.
![Page 13: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/13.jpg)
Soal - 6
Hitunglah luas daerah yang diarsir !
14 cm
![Page 14: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/14.jpg)
Pembahasan : Luas lingkaran
yang diarsir :Lb = ½ r2
= ½ x 22/7 x 7 x 7 = 77 cm2
Lk = r2 = 22/7 x 3,5 x 3,5 = 38,5 cm2
Luas yg diarsir = 77 cm2 - 38,5 cm2 = 38,5 cm2
14 cm
![Page 15: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/15.jpg)
Soal – 7
Pada gambar disamping diketahui besar AOB = 1000 . Hitunglah besar ACB
O
A
B
C
![Page 16: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/16.jpg)
Pembahasan :
• Sudut pusat = 2x sudut kelilingACB = ½ AOB• = ½ x 1000
• = 500
• Jadi besar ACB = 500.
![Page 17: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/17.jpg)
Soal – 8
Pada gambar disamping diketahui besar PRQ = 450 . Hitunglah besar POQ
O
R
PQ
![Page 18: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/18.jpg)
Pembahasan :
PRQ = 500
POQ = 2 x PRQ• = 2 x 450
• = 900
• Jadi besar POQ = 900.
![Page 19: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/19.jpg)
Soal – 9
Pada gambar disamping diketahui besar OAB = 500 . Hitunglah besar :a. OBAb. AOB c. ACB
O
A
B
C
![Page 20: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/20.jpg)
Pembahasan :
a. OBA = OAB ( segitiga sama kaki)
= 500
b. AOB = 1800 – ( 500 + 500 ) = 1800 - 1000
= 800 c. ACB = ½ x OBA = ½ x 800 = 400 .
![Page 21: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/21.jpg)
Soal – 10Pada gambar di samping diketahui besar ACB = 700
dan AED = 600 . Hitunglah besar :a. ADEb. DAC c. CBD
OA
CD
B•E
![Page 22: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/22.jpg)
Pembahasan :
ACB = 700 dan AED = 600
a. ADE = ACD = 700 ( menghadap busur AB.
b. DAC = 180 – ( 70 + 60 ) = 180 - 130 = 500
c. CBD = DAC = 500 (menghadap busur CD.)
![Page 23: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/23.jpg)
Soal – 11
Pada gambar di samping, segiempat ABCD merupakan segiempat tali busur. Panjang AB = 5 cm, BC = 6 cm, CD = 7 cm, AD = 9 cm, dan BD = 11 cm. Hitunglah panjang AC
•
5
9 7
A
B
C
D
O
6
![Page 24: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/24.jpg)
Pembahasan :
AC x BD = ( AB x CD) + ( AD x BC )
AC x 11 = ( 5 x 7 ) + ( 9 x 6 )11 AC = 35 + 5411 AC = 89 AC = 89 : 11 = 8, 09
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Soal – 12Pada gambar di samping, segiempat PQRS merupakan segiempat tali busur. Panjang PQ = 12 cm, QR = 8 cm, SR = 9 cm, PR = 14 cm, dan QS = 13 cm. Hitunglah panjang PS
•6
12
Q
RS
P
O
9
![Page 26: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/26.jpg)
Pembahasan :
PQ x QS = ( PQ x SR ) + ( PS x QR)
12 x 13 = ( 12 x 9 ) + ( PS x 6 )
156 = 108 + 6 PS 6PS = 156 – 108 = 48 PS = 48 : 6 = 8 cm.
![Page 27: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/27.jpg)
Soal-13Pada gambar disamping, besar ABC = 600 dan BCD = 200 . Hitunglah besar AEC
A B
C
D
E
•O
![Page 28: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/28.jpg)
Pembahasan :
ABC = 600
BCD = 200
AEC = ABC - BCD
= 600 - 200
= 400
Jadi, besar AEC = 400
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Soal-14
Pada gambar disamping, besar POR = 1000 dan QOS = 300 . Hitunglah besar PTR .
P Q
R
S
T•O
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Pembahasan :
POR = 1000
QOS = 300
PTR = ½ (POR - QOS)
= ½ ( 1000 - 300 )
= 350
Jadi, besar PTR = 350
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Soal-15
Pada gambar di bawah, garis AB merupakan garis singgung. Panjang OA = 13 cm dan jari-jari OB = 5 cm. Hitunglah panjang garis singgung AB.
BA
O•
![Page 32: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/32.jpg)
Pembahasan :
Perhatikan Δ OAB siku-siku di titik B
AB2 = OA2 - OB2
= 132 - 52
= 169 - 25 = 144AB = √ 144 = 12 cm.Jadi, panjang garis singgung AB =
12 cm.
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Soal 16
M N
A
B
Jika : AM = 7 cm , BN = 3 cm dan AB = 24 cm
Tentukan jarak kedua pusatnya (MN).
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MN2 = AB2 + ( r1 + r2 )2
= 242 + ( 7 + 3 )2
= 576 + 100 = 676MN = √ 676 = 26 cm Jadi, jarak titik pusatnya = 26 cm.
Pembahasan :
M
N
A
B
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Soal 17
M
N
A
B
Jika : AM =4 cm , BN = 2 cm dan MN = 10 cm
Tentukan panjang garis singgung AB.
![Page 36: Latihan Soal Lingkaran](https://reader033.vdocuments.site/reader033/viewer/2022061405/5571f2c949795947648d0db5/html5/thumbnails/36.jpg)
Pembahasan :
AB2 = MN2 -( r1 - r2 )2
= 102 - ( 4 - 2 )2
= 100 – 4 = 96AB = √ 96 = 9,79Jadi, panjang AB = 9,79 cm.
M
N
A
B
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