question_answer

Two circles touch each other internally. Their radii are 2 cm and 3 cm. The biggest chord of the outer 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 :

Here, OA = 10 cm, OB = 3 cm \[\therefore \]      \[AB=\sqrt{{{3}^{2}}-{{1}^{2}}}=\sqrt{8}\,\,\text{cm}\] \[\therefore \] Required length \[=BC=2AB=2\sqrt{8}\,\,\text{cm}=4\sqrt{2}\,\,\text{cm}\]