The radii of two circles are 5cm and 3cm, the distance between

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The radii of two circles are 5cm and 3cm, the distance between their centre is 24 cm. Then the length of the transverse common tangent is

1. 16 cm
2. 15√2 cm
3. 16√2 cm
4. 15 cm

Correct Option: C

On the basis of question we draw a figure of two circles with radii 5cm and 3cm ,

Here , d = 24 cm
We know that , Transverse common tangent = √d² - (r₁ +r₂)²
Transverse common tangent = √(24)² - (5 + 3)⊃
Transverse common tangent = √576 - 64
Transverse common tangent = √512
Transverse common tangent = 16√2cm.