Question : If the radius of two circles is 6 cm and 9 cm and the length of the transverse common tangent is 20 cm, then find the distance between the two centres.
Option 1: 25 cm
Option 2: 22 cm
Option 3: 24 cm
Option 4: 27 cm
Correct Answer: 25 cm
Solution :
According to the question
Length of traverse common target = 20 cm
$r_1$ = 6 cm and $r_2$ = 9 cm
Now,
⇒ Length of traverse common target = $\sqrt{d^{2} - (r_1 + r_2)^{2}}$
⇒ $(20)^{2} = \sqrt{d^{2} - (r1 + r2)^{2}}$
⇒ 400 = $ d^{2} - {225}$
⇒ $d^{2}$ = 225 + 400 = 625
⇒ d = $\sqrt{625}$ = 25 cm
Hence, the correct answer is 25 cm.
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