Question : The distance between the centres of two circles having radii of 8 cm and 3 cm is 13 cm. The length (in cm) of the direct common tangent of the two circles is:
Option 1: 15 cm
Option 2: 16 cm
Option 3: 18 cm
Option 4: 12 cm
Correct Answer: 12 cm
Solution :
Given: AB = 13 cm
AP = 8 cm
BQ = 3 cm
Direct common tangent (PQ) = $\sqrt{d^2-(r_1-r_2)^2}$
= $\sqrt{13^2-(8-3)^2}$
= $\sqrt{13^2-5^2}$
= $\sqrt{169-25}$
= $\sqrt{144}$
= 12 cm
Hence, the correct answer is 12 cm.
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