CDS 2025 · PYQ · Circles / Common Tangent · medium
A circle M of radius 8 cm touches externally with another circle N of radius 16 cm. Let P, Q be the points where the common tangent touches the circles M and N respectively. What is the length of the common tangent PQ?
A.16 cm
B.16√2 cm✓ Correct
C.24 cm
D.24√2 cm
Explanation
Distance between centers = r₁ + r₂ = 8 + 16 = 24 cm (external touching). Length of direct/external common tangent = √(d² - (r₁ - r₂)²) = √(576 - 64) = √512 = 16√2 cm.
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