Question

Two concentric circles are of radii 5 cm and 3 cm find the length of the
chord of the longer circle which touches the smaller circle.​

Answer 1

Step-by-step explanation:

Let O be the centre of the concentric circle of radii 5 cm and 3 cm respectively. Let AB be a chord of the larger circle touching the smaller circle at P.

Then

AP=PB and OP⊥AB

Applying Pythagoras theorem in △OPA, we have

OA^2=OP^2+AP^2

⇒25=9+AP^2

⇒AP^2=16⇒AP=4 cm

∴AB=2AP=8 cm

Answer 2

Answer:

Let O be the centre of the concentric circle of radii 5 cm and 3 cm respectively. Let AB be a chord of the larger circle touching the smaller circle at P.

Then

AP=PB and OP⊥AB

Applying Pythagoras theorem in △OPA, we have

${oa}^{2} = {op}^{2} + {ap}^{2}$

$25 = 9 + {ap}^{2}$

$25 - 9 = {ap}^{2}$

$16 = {ap}^{2}$

$\sqrt{16 =} ap$

$4 \: cm = ap$

∴AB=2AP=8 cm