A chord AB of length 12 cm is common to two circles with diameters 13 cm and 15 cm, respectively. Find the distance between the centers of the circles.
Show answer & explanation
Correct answer: B
Explanation
Chord = 12 cm ⇒ Half-chord = 6 cm
Radii = 13/2 = 6.5 cm, 15/2 = 7.5 cm
Distance from the center to the chord = √(r² − (l/2)²)
For the first circle:
d₁ = √(6.5² − 6²) = √(42.25 − 36) = √6.25 = 2.5
For the second circle:
d₂ = √(7.5² − 6²) = √(56.25 − 36) = √20.25 = 4.5
Distance between the centers = d₁ + d₂ = 2.5 + 4.5 = 7 cm