Two circles with radii 37.5 cm and 13.5 cm touch each other externally. The length of the direct common tangent is
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Correct answer: B
Explanation
r₁ = 37.5 cm, r₂ = 13.5 cm
The two circles touch externally ⇒ Distance between their centers d = r₁ + r₂ = 51
Length of the direct common tangent = √(d² − (r₁ − r₂)²)
= √(51² − (37.5 − 13.5)²)
= √(2601 − 24²)
= √(2601 − 576)
= √2025
= 45 cm