Question : The length of the common tangent PQ for two circles touching externally is 16 cm. If the radius (OP) of the bigger circle is 20 cm, then the radius (RQ) of the smaller circle is:
Option 1: 3.2 cm
Option 2: 3.6 cm
Option 3: 3.5 cm
Option 4: 3.8 cm
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Correct Answer: 3.2 cm
Solution :
Given: The length of the common tangent PQ for two circles touching externally is 16 cm and the radius (OP) of the bigger circle is 20 cm.
We know, the length of the common tangent = $2×\sqrt{R×r}$, where $R$ and $r$ are radii of the bigger and smaller circle respectively.
According to the question,
$2×\sqrt{20×r}=16$
$⇒\sqrt{20×r}=8$
$⇒20r=64$ (squaring both sides)
$⇒r=\frac{64}{20}$
$\therefore r=3.2$ cm.
Hence, the correct answer is 3.2 cm.
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