Question

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

• A. 10 cm
• B. 6 cm
• C. 12 cm
• D. 8 cm

Answer 1

The correct option is D

8 cm

Let the two concentric circles with centre O.

AB be the chord of the larger circle which touches the smaller circle at point P.

$\therefore$ AB is tangent to the smaller circle to the point P.

$\Rightarrow$ OP $\perp$ AB
By Pythagoras theorem in $\Delta$OPA,

$O{A}^2=A{P}^2+O{P}^2$

$\Rightarrow 5^2=A{P}^2+3^2$

$\Rightarrow A{P}^2=25–9$

$\Rightarrow$ AP = 4 cm

In $\Delta$OPB,

Since OP $\perp$ AB,

AP = PB (Perpendicular from the centre of the circle bisects the chord)

AB = 2AP = 2 $\times$ 4 = 8 cm

$\therefore$ The length of the chord of the larger circle is 8 cm.