Question

Two concentric circles are of radii 5cm and 3cm find the length of the chord of

Answer 1

Answer:

Let O be the centre of the concentric circle of radii 55 cm and 33 cm respectively. Let ABAB be a chord of the larger circle touching the smaller circle at PP.

Then

AP=PBAP=PB and OP \bot ABOP⊥AB

Applying Pythagoras theorem in \triangle OPA△OPA, we have

${ OA }^{ 2 }={ OP }^{ 2 }+{ AP }^{ 2 }OA</p><p>2</p><p> =OP </p><p>2</p><p> +AP </p><p>2</p><p> </p><p></p><p>\Rightarrow\quad 25=9+{ AP }^{ 2 }⇒25=9+AP </p><p>2</p><p> </p><p></p><p>\Rightarrow\quad { AP }^{ 2 }=16\Rightarrow AP=4 \ cm⇒ AP$

2

=16⇒AP=4 cm

\therefore\quad AB=2AP=8 \ cm∴ AB=2AP=8 cm