Question : Two circles touch each other externally at any point C. PQ is the direct common tangent to both the circles touching the circles at point P and point Q. If the radii of the circles are 36 cm and 16 cm, respectively, then the length of PQ is:
Option 1: 42 cm
Option 2: 24 cm
Option 3: 48 cm
Option 4: 36 cm
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Correct Answer: 48 cm
Solution :
$R = 36$ cm
$r = 16$ cm
$\therefore$ PQ = $\sqrt{d^2-(R-r)^2}$
= $\sqrt{(R+r)^2-(R-r)^2}$
= $\sqrt{(R^2+r^2+2Rr-(R^2-2Rr+r^2)}$
= $\sqrt{4Rr}$
= $\sqrt{4×36×16}$
= $48$ cm
Hence, the correct answer is 48 cm.
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