The lengths of a common external tangent and a common internal tangent to two circles are 8 cm and 6 cm, respectively. If the distance between their centers is 10 cm, what are the radii of the two circles?
Show answer & explanation
Correct answer: C
Explanation
Given:
External tangent = 8 cm
Internal tangent = 6 cm
Distance between centers d = 10 cm
Formula:
External tangent² = d² − (r₁ − r₂)²
Internal tangent² = d² − (r₁ + r₂)²
8² = 10² − (r₁ − r₂)²
6² = 100 − (r₁ − r₂)²
(r₁ − r₂)² = 36
r₁ − r₂ = 6
6² = 10² − (r₁ + r₂)²
36 = 100 − (r₁ + r₂)² r₂)²
(r₁ + r₂)² = 64
r₁ + r₂ = 8
r₁ − r₂ = 6
r₁ + r₂ = 8
2r₁ = 14
r₁ = 7
r₂ = 1
The radii of the two circles = 7 cm and 1 cm