Question : The Radii of the two circles are 20 cm and 4 cm. Length of the direct common tangent is 30 cm. What is the distance between their centres?
Option 1: 36 cm
Option 2: 38 cm
Option 3: 34 cm
Option 4: 32 cm
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Correct Answer: 34 cm
Solution :
Given: $r_1=20$ and $r_2=4$
Let $x$ be the distance between two centres.
We know that,
Direct common tangent = $\sqrt{d^2-(r_1-r_2)^2}$, where $d$ is the distance between the centres and $r_1$ and $r_2$ are the radii of the circles.
⇒ $30=\sqrt{x^2-(20-4)^2}$
⇒ $30=\sqrt{x^2-16^2}$
⇒ $900=x^2-256$
⇒ $x^2=1156$
$\therefore x=34$
Hence, the correct answer is 34 cm.
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