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.

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.
$\therefore$ AB is tangent to the smaller circle to the point P.
$\Rightarrow OP\perp AB$
By Pythagoras theorem in $\Delta$ OPA,
$O{A}^2=A{P}^2+O{P}^2$
$\Rightarrow 5^2=A{P}^2+3^2$
$\Rightarrow A{P}^2=25-9$
$\Rightarrow AP=4$
In $\Delta$ OPB,
Since OP $\perp$ AB,
AP = PB ($\because$ 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.