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Diketahui dua buah lingkaran dengan jarak kedua pusat lingkaran 15 cm, jari-jari lingkaran besar 5 cm,

Rani Maharani

Soal

Diketahui dua buah lingkaran dengan jarak kedua pusat lingkaran 15 cm, jari-jari lingkaran besar 5 cm, dan jari-jari lingkaran kecil 4 cm. Tentukan panjang garis singgung persekutuan dalamnya!

Pembahasan

Diketahui:

Jarak kedua pusat lingkaran (p) = 15 cm

Jari-jari lingkaran besar (r1) = 5 cm

Jari-jari lingkaran kecil (r2) = 4 cm

Ditanyakan:

Panjang garis singgung persekutuan dalam kedua lingkaran (d)

Rumus:

d = √(p² - (r1-r2)²)

Substitusikan nilai yang diketahui ke dalam rumus:

d = √(15² - (5-4)²)

d = √(225 - 1)

d = √224

d = 14.97 cm

Jadi, panjang garis singgung persekutuan dalam kedua lingkaran tersebut adalah 14.97 cm.

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