Question
Download Solution PDFThe centres of two circles are 84 cm apart. If the radii of these two circles are 38 cm and 26 cm, respectively, then which of the following options gives the length (in cm) of a direct common tangent of these two circles?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Distance between the centers = 84 cm
Radius of first circle (r1) = 38 cm
Radius of second circle (r2) = 26 cm
Formula used:
Length of direct common tangent (L) = √(d2 - (r1 - r2)2)
Where d = distance between the centers, r1 and r2 are the radii of the circles.
Calculation:
⇒ L = √(842 - (38 - 26)2)
⇒ L = √(7056 - 122)
⇒ L = √(7056 - 144)
⇒ L = √6912
⇒ L = 48√3 cm
∴ The length of the direct common tangent is approximately 48√3 cm.
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