Question

In the given figure, O is the centre of two concentric circles of radii 6 cm and 10 cm. AB is a chord of outer circle which touches the inner circle. The length of chord AB is

(a) 8 cm (b) 14 cm (c) 16 cm (d) $\sqrt{136}$ cm

Answer 1

Let the two concentric circles with centre O.

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

∴ AB is tangent to the smaller circle to the point P.

⇒$OP\perp AB$

By Pythagoras theorem in $\Delta$OPA,

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

⇒${10}^2=A{P}^2+6^2$

⇒$A{P}^2=100-36=64$

⇒$AP=8$

In $\Delta$OPA,

Since $OP\perp AB$,

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

$AB=2AP=2\times 8=16$ cm

∴ The length of the chord of the larger circle is 16 cm.