Question

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. $3\sqrt{2}m$
• C. $2\sqrt{3}cm$
• D. $4\sqrt{2}m$

Answer 1

The correct option is D $4\sqrt{2}m$

Given two cicrcles with centers C1 and C2 of radii 2 cm and 3 cm touch internally .

the LONGEST chord AB of circle with center C2 must be a tangent to the circle with center C1.

from the figure, clearly the length of line segment C1C2 is 1 cm.

$⟹AB=2\times xfrompythagorastheorem,x=\sqrt{3^2-1^2}=\sqrt{9-1}=\sqrt{8}=2\sqrt{2}⟹AB=2x⟹AB=2\times 2\sqrt{2}⟹AB=4\sqrt{2}$

Ans: D