question_answer

The distance between the centres of two circles having radii 4.5 cm and 3.5 cm, respectively is 10 cm. What is the length of the transverse common tangent of these circles?

A) 8 cm    

B)  7 cm

C)  6 cm   

D)  None of the above

Correct Answer: C

Solution :

From figure, length of the transverse common tangent of these circles

\[=\sqrt{\begin{align}   & \text{Distance}\,\,\text{between}\,\,\text{tyhe}\,\,\text{centres}\,\,\text{of}\,\,\text{circles}{{\text{)}}^{\text{2}}} \\  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-\,\,{{\text{(Sum}\,\,\text{of}\,\,\text{radius)}}^{\text{2}}} \\ \end{align}}\]

\[=\sqrt{{{10}^{2}}-{{(4.5+3.5)}^{2}}}=\sqrt{{{10}^{2}}-{{8}^{2}}}=\sqrt{36}=6\,\,\text{cm}\]