Two circles have radii 8 cm and 6 cm. The distance between their centers is 18 cm. What is the length of their common internal tangent segment?
Show answer & explanation
Correct answer: A
Explanation
Given:
r₁ = 8 cm
r₂ = 6 cm
Distance between centers d = 18 cm
Formula:
Length of internal common tangent segment = √[d² − (r₁ + r₂)²]
= √[18² − (8 + 6)²]
= √[324 − 14²]
= √[324 − 196]
= √128
= 8√2
Internal common tangent segment = 8√2 cm