Question
Download Solution PDFRadii of two circles are 12 cm and 5 cm. Distance between their centres is 25 cm. What is the length of the direct common tangent?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Radii of two circles are 12 cm and 5 cm. Distance between their centres is 25 cm.
Formula used:
Length of the direct common tangent of two circles = \(\sqrt {D^2 - (r_1 - r_2)^2}\) (D = Distance between their centres, r1 = radius of the bigger circle, and r2 = radius of the smaller
Calculation:
Let the centres be at P and Q.
QN = Radius of the bigger circle = 12 cm
PM = Radius of the smaller circle = 5 cm
Let MN be the direct common tangent.
According to the formula,
Length of MN
⇒ \(\sqrt {25^2 - (12 - 5)^2}\)
⇒ \(\sqrt {576}\)
⇒ 24 cm
∴ The length of the direct common tangent is 24 cm.
Last updated on May 28, 2025
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