Question
Download Solution PDFThe distance between the centres of the two circles, with radii 3 cm and 2 cm, respectively, is 13 cm. The length (in cm) of a transverse common tangent is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The distance between the centers of the two circles, with radii 3 cm and 2 cm, respectively, is 13 cm.
Formula Used:
Length of transverse common tangent = \( \sqrt{d^2 - (r_1 + r_2)^2} \)
Where,
d = distance between the centres of the two circles
r1 = radius of the first circle
r2 = radius of the second circle
Calculation:
d = 13 cm
r1 = 3 cm
r2 = 2 cm
⇒ Length of transverse common tangent = \( \sqrt{13^2 - (3 + 2)^2 } \)
⇒ Length of transverse common tangent = \( \sqrt{169 - 25} \)
⇒ Length of transverse common tangent = \( \sqrt{144} \)
⇒ Length of transverse common tangent = 12 cm
∴ The correct answer is option (4).
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