Two circles with their centres at O and P and radii 8 cm

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Two circles with their centres at O and P and radii 8 cm and 4 cm respectively touch each other externally. The length of their common tangent is

1. 8.5 cm.
2. 8 cm.
  √2
3. 8√2 cm.
4. 8 cm.

Correct Option: C

We know that , Common tangent = √(Direct between centres)² - (r₁ - r₂)²
Common tangent = √(8 + 4)² - (8 - 4)²
Common tangent = √12² - 4²
Common tangent = √144 - 16 = √128
Common tangent = 8√2 cm

8	cm.
√2