Question

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

Answer 1

Radius of big circle,
$OA=OB=5cm$
Radius of small circle, $OP=3cm$
Angle between radius and tangent is ${90}^{\circ }$
$\therefore \angle OPA=\angle OPB={90}^{\circ }$
($\because$ Chord AB is tangent to small circle )
Now , in $\perp △OPA,\angle OPA={90}^{\circ }$
$O{P}^2+A{P}^2=O{A}^2$
$(3{)}^2+A{P}^2=(5{)}^2$
$9+A{P}^2=25$
$\therefore A{P}^2=25-9$
$A{P}^2=16$
$\therefore AP=4cm$
Similarly , in $\perp △OPB,PB=4cm$
$\therefore$ Length of chord , $AB=AP+PB=4+4$
$\therefore$ chord , $AB=8cm$