Question
Download Solution PDFIf the radii of two circles be 8 cm and 6 cm and the length of the transverse common tangent be 14 cm, then the distance between the two centres is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Radius of the first circle (r1) = 8 cm
Radius of the second circle (r2) = 6 cm
Length of the transverse common tangent (L) = 14 cm
Formula used:
Distance between the centers (d) = \(\sqrt{(r_1 + r_2)^2 + L^2}\)
Calculations:
d = \(\sqrt{(8 + 6)^2 + 14^2}\)
⇒ d = \(\sqrt{14^2 + 14^2}\)
⇒ d = \(\sqrt{2 \times 14^2}\)
⇒ d = \(\sqrt{2} \times 14\)
⇒ d = 14√2 cm
∴ The correct answer is option (4).
Alternate MethodGiven:
The length of the transverse common tangent = AB = 14 cm
The distance between the two centres = D
The radius of two circles r1 = 8 cm, and r2 = 6 cm
Formula used:
\(AB=\sqrt{D^2-(r_1 + r_2)^2}\)
Calculation:
\(14=\sqrt{D^2-(8+6)^2}\)
⇒ \(14^2=D^2-14^2\)
⇒ \(196=D^2-196\)
⇒ \(D^2=392\)
⇒ \(D=\sqrt{392}\)
⇒ \(D=14\sqrt{2}\)
∴ The distance between the two centres is 14√2 cm.
Last updated on Dec 9, 2024
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