Question

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. $4\sqrt{2}$ cm
• B. $4\sqrt{3}$ cm
• C. $6\sqrt{3}$ cm
• D. $8\sqrt{2}$ cm

Answer 1

The correct option is D $8\sqrt{2}$ cm

$A$ and $B$ are the centres of outer and inner circles.
$BC=4$ cm and $AO=6$ cm
$\therefore AC=OC-OA$
$=(8-6)cm=2$ cm
Longest chord is $DE$ or $DC$
$D{C}^2=A{D}^2-A{C}^2$
$=6^2-2^2=32$
$\therefore DC=4\sqrt{2}$
$\therefore DE=8\sqrt{2}$ cm.