Question : Two circles touch each other externally. The radius of the first circle with centre A is 18 cm. The radius of the second circle with centre B is 8 cm. Find the length of their common tangent CD.
Option 1: 23 cm
Option 2: 26 cm
Option 3: 24 cm
Option 4: 25 cm
Correct Answer: 24 cm
Solution :
Given: The radius of the first circle, $r_1$ = 18 cm
The radius of the second circle, $r_2$ = 8 cm
We know that,
Length of the direct common tangent
$=2 \sqrt{r_1 \times r_2}$
$=2 \sqrt{18 \times 8}$
$=2 \sqrt{144}$
$=2 \times 12$
$= 24$
Hence, the correct answer is 24 cm.
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