Question : The radii of the two circles are 9 cm and 4 cm, the distance between their centres is 13 cm, then the length of the direct common tangent is:
Option 1: 8 cm
Option 2: 14 cm
Option 3: 12 cm
Option 4: 16 cm
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Correct Answer: 12 cm
Solution :
Given: d = PQ = 9 + 4 = 13 cm
$r_1$ = 9 cm
$r_2$ = 4 cm
Direct common tangent (CD)
= $\sqrt{d^2-(r_1-r_2)^2}$
= $\sqrt{13^2-(9-4)^2}$
= $\sqrt{13^2-5^2}$
= $\sqrt{169-25}$
= $\sqrt{144}$
= 12 cm
Hence, the correct answer is 12 cm.
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