Two circles touch each other internally. Their radii are 2 cm and 3 cm. The biggest chord of the greater circle which is outside the inner circle is of length |
A) \[2\sqrt{2}\,cm\]
B) \[3\sqrt{2}\,cm\]
C) \[2\sqrt{3}\,cm\]
D) \[4\sqrt{2}\,cm\]
Correct Answer: D
Solution :
Let O and O' be the centres of greater and smaller circles, respectively. |
\[\therefore \] \[OM=O'M=OO'=2-1=1\] |
In \[\Delta AOM,\]\[A{{M}^{2}}=O{{A}^{2}}-O{{M}^{2}}\] |
\[=9-1=8\] |
\[\Rightarrow \] \[AM=2\sqrt{2}\] |
\[\therefore \] Length of biggest chord, \[AB=2\cdot AM=4\sqrt{2}\] |
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