Roboguru

Pertanyaan

Tentukan panjang garis singgung persekutuan dalam kedua lingkaran berikut!

a.  begin mathsize 14px style r subscript 1 equals 5 space cm space space space space space r subscript 2 equals 7 space cm space space space space space dan space space space space s equals 13 space cm end style

b   begin mathsize 14px style r subscript 1 equals 4 space cm space space space space space r subscript 2 equals 3 space cm space space space space space dan space space space space s equals 25 space cm end style

c.  begin mathsize 14px style r subscript 1 equals 4 space cm space space space space space r subscript 2 equals 2 space cm space space space space space dan space space space space s equals 10 space cm end style

d.  begin mathsize 14px style r subscript 1 equals 8 space cm space space space space space r subscript 2 equals 4 space cm space space space space space dan space space space space s equals 15 space cm end style

e.  begin mathsize 14px style r subscript 1 equals 7 space cm space space space space space r subscript 2 equals 3 space cm space space space space space dan space space space space s equals 15 space cm end style

H. Hermawan

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Pembahasan

Jika diketahui begin mathsize 14px style r subscript 1 comma space r subscript 2 comma space s end style berturut-turut adalah panjang jari-jari lingkaran pertama, panjang jari-jari lingkaran kedua, dan jarak pusat kedua lingkaran, maka rumus menentukan panjang garis persekutuan dalam dua lingkaran begin mathsize 14px style open parentheses d close parentheses end style adalah

begin mathsize 14px style d equals square root of s squared minus open parentheses r subscript 1 plus r subscript 2 close parentheses squared end root end style

a.  begin mathsize 14px style r subscript 1 equals 5 space cm comma space space space space space space r subscript 2 equals 3 space cm comma space space space space space space space space s equals 13 space cm end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row d equals cell square root of s squared minus left parenthesis r subscript 1 plus r subscript 2 right parenthesis squared end root end cell row d equals cell square root of 13 squared minus left parenthesis 5 plus 7 right parenthesis squared end root end cell row d equals cell square root of 13 squared minus left parenthesis 12 right parenthesis squared end root end cell row d equals cell square root of 169 minus 144 end root end cell row d equals cell square root of 25 end cell row d equals cell 5 space cm end cell end table end style

Dengan demikian panjang garis singgung persekutuan dalam dua lingkaran adalah begin mathsize 14px style 5 space cm end style.

b.  begin mathsize 14px style r subscript 1 equals 4 space cm comma space space space space space space r subscript 2 equals 3 space cm comma space space space space space space space space s equals 25 space cm end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row d equals cell square root of s squared minus left parenthesis r subscript 1 plus r subscript 2 right parenthesis squared end root end cell row d equals cell square root of 25 squared minus left parenthesis 4 plus 3 right parenthesis squared end root end cell row d equals cell square root of 25 squared minus left parenthesis 7 right parenthesis squared end root end cell row d equals cell square root of 625 minus 49 end root end cell row d equals cell square root of 576 end cell row d equals cell 24 space cm end cell end table end style

Dengan demikian panjang garis singgung persekutuan dalam dua lingkaran adalah begin mathsize 14px style 24 space cm end style.

c.  begin mathsize 14px style r subscript 1 equals 4 space cm comma space space space space space space r subscript 2 equals 2 space cm comma space space space space space space space space s equals 10 space cm end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row d equals cell square root of s squared minus left parenthesis r subscript 1 plus r subscript 2 right parenthesis squared end root end cell row d equals cell square root of 10 squared minus left parenthesis 4 plus 2 right parenthesis squared end root end cell row d equals cell square root of 10 squared minus left parenthesis 6 right parenthesis squared end root end cell row d equals cell square root of 100 minus 36 end root end cell row d equals cell square root of 64 end cell row d equals cell 8 space cm end cell end table end style

Dengan demikian panjang garis singgung persekutuan dalam dua lingkaran adalah begin mathsize 14px style 8 space cm end style.

d.  begin mathsize 14px style r subscript 1 equals 8 space cm comma space space space space space space r subscript 2 equals 4 space cm comma space space space space space space space space s equals 15 space cm end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row d equals cell square root of s squared minus left parenthesis r subscript 1 plus r subscript 2 right parenthesis squared end root end cell row d equals cell square root of 15 squared minus left parenthesis 8 plus 4 right parenthesis squared end root end cell row d equals cell square root of 15 squared minus left parenthesis 12 right parenthesis squared end root end cell row d equals cell square root of 225 minus 144 end root end cell row d equals cell square root of 81 end cell row d equals cell 9 space cm end cell end table end style

Dengan demikian panjang garis singgung persekutuan dalam dua lingkaran adalah begin mathsize 14px style 9 space cm end style .

e.  begin mathsize 14px style r subscript 1 equals 7 space cm comma space space space space space space r subscript 2 equals 3 space cm comma space space space space space space space space s equals 15 space cm end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row d equals cell square root of s squared minus left parenthesis r subscript 1 plus r subscript 2 right parenthesis squared end root end cell row d equals cell square root of 15 squared minus left parenthesis 7 plus 3 right parenthesis squared end root end cell row d equals cell square root of 15 squared minus left parenthesis 10 right parenthesis squared end root end cell row d equals cell square root of 225 minus 100 end root end cell row d equals cell square root of 125 end cell row d equals cell 5 square root of 5 space cm end cell end table end style

Dengan demikian panjang garis singgung persekutuan dalam dua lingkaran adalahbegin mathsize 14px style 5 square root of 5 space cm end style.

 

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