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Tentukan jarak antara kedua titik pusat lingkaran, jika diketahui panjang garis singgung persekutuan

Rani Maharani

Soal

Tentukan jarak antara kedua titik pusat lingkaran, jika diketahui panjang garis singgung persekutuan luarnya 24 cm dengan jari-jari lingkaran PA = II cm dan BQ = 4 cm.

Pembahasan

Misalkan P dan Q adalah pusat lingkaran PA dan BQ secara berurutan. Jarak antara kedua titik pusat lingkaran adalah jarak antara titik P dan Q, yang dapat dihitung sebagai berikut:

\begin{aligned} � � & = � � + � � \\ = 2 \times r + 2 \times r \\ = 4 \times r \end{aligned}

Dalam kasus ini, jarak antara kedua titik pusat lingkaran adalah:

\begin{aligned} � � & = 4 \times r \\ = 4 \times (PA + BQ) \\ = 4 \times (11 + 4) \\ = 60 \end{aligned}

Jadi, jarak antara kedua titik pusat lingkaran adalah 60 cm.

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