Pembinaan kls 9ke 1
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1. Sebuah lingkaran berdiameter 12 cm. Dan sebuah titik T diluar lingkaran yang berjarak 10 cm dari pusat lingkaran.Hitung berapa panjang garis singgung lingkaran dari titik T !
OT
A
6 cm
10 cm
AT2 = OT2 - r2
= 102 - 62
= 100 - 36= 64
AT= 8 cm
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2. Sebuah lingkaran berjari-jari 5cm. Panjang garis singgung lingkaran dari titik T diluar lingkaran adalah 12cm. Berapa jarak titik T ke pusat lingkaran?
OT
A
5 cm12 cm
OT2 = AT2 + r2
= 122 + 52
= 144 + 25= 169
OT = 13 cm
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3. Jarak pusat lingkaran o dan titik T diluar lingkaranadalah 15 cm. Panjang garis singgung lingkaran dari titik T diluar lingkaran adalah 12cm. Berapa jari-jari lingkaran o?
OT
A12 cm
15 cm
r2 = OT2 - AT2
= 152 – 122
= 225 - 144= 81
r = 9 cm
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4.Dua lingkaran saling lepas berjari-jari 8 cm dan 3 cm.Jarak kedua pusat lingkaran 13 cm. Tentukan panjang garis singgung persekutuan luar !
A B
R=8
r=3
D
C
13
DC2 = AB2 – (R-r)2
DC2 = 132 – (8-3)2
DC2 = 169 – 25
DC2 = 144DC = 12 cm
garis singgung persekutuan luar = 12 cm
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5. Dua lingkaran saling lepas berjari-jari 4 cm dan 2 cm.Jarak kedua pusat lingkaran 10 cm. Tentukan panjang garis singgung persekutuan dalam!
AB
R=4
r = 2
K
M
10
KM2 = AB2 – (R+r)2
KM2 = 102 – (4+2)2
KM2 = 100 – 36KM2 = 64KM = 8 cm
garis singgung persekutuan dalam = 8 cm
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Dua pipa berjari – jari 7 cm. Diikat dengan tali. Berapa cm tali minimal yang melilit kedua pipa tersebut ?
7 cm 7 cm
P.Lilitan = Kll. Lingkaran + 2.diameter
P.Lilitan = π.d + 2.dP.Lilitan = 22/7.14 +2. 14
P.Lilitan = 44 + 28P.Lilitan = 72 cm
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7. Tiga pipa berjari – jari 7 cm. Diikat dengan tali. Berapa cm tali minimal yang melilit ketiga pipa tersebut ?
PQ
R
A
BC
D
EF
P.Lilitan = Kll. Lingkaran + 3. diameter
P.Lilitan = π.d + 3.dP.Lilitan = 22/7.14 +3. 14
P.Lilitan = 44 + 42P.Lilitan = 86 cm
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P.Lilitan = Kll. Lingkaran + 4. diameter
P.Lilitan = π.d + 4.d
P.Lilitan = 22/7.14 +4. 14
P.Lilitan = 44+ 56
P.Lilitan = 100 cm
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X
8
X
X
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b. sl2 = 242 – (12-5)2
sl2 = 576 – 49
sl2 = 527 sl = 527
a. sd2 = 242 – (12+5)2
sd2 = 576 – 289
sd2 = 287
sd = 287
9
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10
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a. OP2 = sl2 + (R-r)2
OP2 = 122 + (9-4)2
OP2 = 144 + 25
OP2 = 169 OP = 13 cm
I
II4 cm
12 cm
5cm12 cm
b. Luas I = 12 x 4 = 48
Luas II = 12 x 5 = 302
Luas I dan II = 48 +30 = 78
Luas ABCD= 78 x 2 = 156 cm2
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11
(R+r)2 = Jarak pusat2 - sd2
sd2 = Jarak pusat2 – (R+r)2
(R+r)2 = 262 - 242
(R+r)2 = 676 - 576
(R+r)2 = 100 (R+r) = 10
6+r = 10
r = 4 cm
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12
P.Lilitan = Kll. Lingkaran + 2.diameter
144 = π.d+ 2.d 144 = 22/7.d+ 2.d 144 = 22/7.d+ 14/7.d 144 = 36/7.d 144 : 36/7 = d 144 x 7/36 = d 28= d r = 14 cm
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13
P.Lilitan = Kll. Lingkaran + 6.diameter
P.Lilitan = 3,14 . 48 + 6 . 48P.Lilitan = 438,72 cm
π= 3,14
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1300
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Segi empat tali busur yang kedua diagonalnya merupakan diameter saling berpotongan tegak lurus akan membentuk bangun…………..
persegi
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Segi empat tali busur yang kedua diagonalnya merupakan diameter akan membentuk bangun…………..Persegi panjang
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a
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Hitunglah keliling daerah yang diarsir pada gambar berikut
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