Question : The radii of the two circles are 11 cm and 3 cm. The distance between their centres is 17 cm. What is the length of the direct common tangent?
Option 1: 12 cm
Option 2: 14 cm
Option 3: 16 cm
Option 4: 15 cm
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Correct Answer: 15 cm
Solution :
The radii of two circles are 11 cm and 3 cm.
The distance between their centres is 17 cm.
Length of the direct common tangent of two circles = $\sqrt{D^2-({r_{1}}-r{_{2}})^2}$
D = Distance between their centres
$r{_{1}}$ = radius of the bigger circle
$r{_{2}}$ = radius of the smaller circle
Let the centres be at P and Q.
ON = Radius of the bigger circle = 11 cm
PM = Radius of the smaller circle = 3 cm
Let MN be the direct common tangent.
According to the formula,
Length of MN
= $\sqrt{17^2−(11−3)^2}$
= $\sqrt{289−64}$
= 15 cm
Hence, the correct answer is 15 cm.
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