question_answer

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, \[AB=2\cdot AM=4\sqrt{2}\]