Two circles C₁ and C₂ touch each other externally. The radius of C₁ is 16 cm and the radius of C₂ is 8 cm. Find the length (in cm) of their common tangent.

Question

Accepted Answer

Let the centers of circles C₁ and C₂ be O₁ and O₂, with radii r₁ = 16 cm and r₂ = 8 cm, respectively. The distance between the centers, O₁O₂, is r₁ + r₂ = 16 + 8 = 24 cm (since they touch externally).

The length of the common external tangent (L) between two circles of radii r₁ and r₂, with centers separated by distance d, is given by:

L = √[d² - (r₁ - r₂)²]

Here, d = 24 cm, r₁ - r₂ = 16 - 8 = 8 cm.

So,
L = √[24² - 8²] = √[576 - 64] = √512 = √(256 × 2) = 16√2 cm.

Therefore, the length of their common tangent is 16√2 cm.

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