Question : The distance between the centres of two circles with radii of 9 cm and 16 cm is 25 cm. The length of the segment of the tangent between them is:
Option 1: $24\ \text{cm}$
Option 2: $25\ \text{cm}$
Option 3: $\frac{50}{3}\ \text{cm}$
Option 4: $12\ \text{cm}$
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Correct Answer: $24\ \text{cm}$
Solution : Given: $r_1=16$ cm, $r_2=9$ cm Distance between two centres = 25 cm We know, the required length of the tangent = $\sqrt{\text{Distance between two centres}^2-(r_1-r_2)^2}$ = $\sqrt{25^2-(16-9)^2}$ = $\sqrt{625-49}$ = $\sqrt{576}$ = $24$ cm Hence, the correct answer is $24\ \text{cm}$.
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