question_answer

Two circles touch each other internally. Their radii are 4 cm and 6 cm. What is the length of the longest chord of the outer circle which is outside the inner circle?

A)  \[4\sqrt{2}\,\,\text{cm}\]

B)  \[4\sqrt{3}\,\,\text{cm}\]

C)  \[6\sqrt{3}\,\,\text{cm}\]

D)  \[8\sqrt{2}\,\,\text{cm}\]

Correct Answer: A

Solution :

OA = Diameter of inner circle = 4 cm

and \[OB=AB-OA=6-4=2\,\,\text{cm}\]

PQ and AB are two chord of outer circle,

\[\therefore \]      \[OA\times OB=OP\times OQ\]   \[(\because OP=OQ)\]

\[\Rightarrow \]   \[4\times 2=O{{P}^{2}}\]

\[\Rightarrow \]   \[OP=2\sqrt{2}\,\,\text{cm}\]

\[\therefore \]      \[PQ=2\times 2\sqrt{2}=4\sqrt{2}\,\,\text{cm}\]