Question : In two circles centred at O and O’, the distance between the centres of both circles is 17 cm. The points of contact of a direct common tangent between the circles are P and Q. If the radii of both circles are 7 cm and 15 cm, respectively, then the length of PQ is equal to:
Option 1: 15 cm
Option 2: 17 cm
Option 3: 10 cm
Option 4: 22 cm
Correct Answer: 15 cm
Solution :
Length of direct common tangent =$\sqrt{(\text{Distance between centre of circles })^2-\text{(Difference between radius of two circles})^2}$
Square of difference between radius of two circles = $(15 -7)^2 = 8^2 = 64$
Length of direct common tangent, PQ = $\sqrt{17^2 - 64} = \sqrt{289-64} = \sqrt{225} = 15$
Hence, the correct answer is 15 cm.
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