Question : The distance between the centres of two circles is 61 cm and their radii are 35 cm and 24 cm. What is the length (in cm) of the direct common tangent to the circles?
Option 1: 60
Option 2: 54
Option 3: 48
Option 4: 72
Correct Answer: 60
Solution :
The length of the direct common tangent between two circles,
$=\sqrt{d^2 - (r_1 - r_2)^2}$, where $r_1,r_2$ are the radii of the circles and $d$ is the distance between their centres.
Given that $d$ = 61 cm, $r_1$ = 35 cm, and $r_2$ = 24 cm
$=\sqrt{(61)^2 - (35 - 24)^2} = \sqrt{3721 - 121} = \sqrt{3600}=60$ cm
Hence, the correct answer is 60.
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