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 |
\[=\sqrt{\begin{align} & \text{Distance}\,\,\text{between}\,\,\text{tyhe}\,\,\text{centres}\,\,\text{of}\,\,\text{circles}{{\text{)}}^{\text{2}}} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-\,\,{{\text{(Sum}\,\,\text{of}\,\,\text{radius)}}^{\text{2}}} \\ \end{align}}\] |
\[=\sqrt{{{10}^{2}}-{{(4.5+3.5)}^{2}}}=\sqrt{{{10}^{2}}-{{8}^{2}}}=\sqrt{36}=6\,\,\text{cm}\] |
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