Question

Two concentric circles are of radii 3 cm and 5 cm respectively.The length of a chord of the outer circle which is a tangent to the inner circle is

Answer 1

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

⇒AP

2

=16⇒AP=4 cm

∴AB=2AP=8 cm

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Answer 2

Answer:

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

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