Question

Two concentric circles of radii 5 cm and 3cm are drawn. Find the length of the chord of the larger circle which touches the smaller circle.

• A. 10 cm
• B. 8 cm
• C. 4 cm
• D. 12 cm

Answer 1

The correct option is B 8 cm

In two concentric circles, the chord of the bigger circle, that touches the smaller circle is a tangent to the smaller circle. Since the radius is perpendicular to the tangent, In bigger circle the radius bisect the chord at the point of contact with the smaller circle.
So, AP = PB
Chord of bigger circle = AB = AP+PB
(or) AB = 2AP
Given, OA = 5 cm [radius of bigger circle]
and OP = 3 cm [radius of smaller circle]
By pythagoras theorm,
${OA}^2$ = ${OP}^2$ + ${AP}^2$
${AP}^2$ = ${OA}^2$ - ${OP}^2$
=$5^2$ - $3^2$
${AP}^2$= 25-9
AP = $\sqrt{16}$
AP = 4 cm
So, AB = 2AP = 2 $\times$ 4 = 8 cm