Question

Q.6
Two concentric circles are of the radii 5 cm and 3 cm. Find the length of the chord of the
larger circle which touches the smaller circle.​

Answer 1

Given :-

• Radius of circle 1 = 5cm
• Radius of circle 2 = 3cm

To Find :-

• Length of the chord of the larger circle.

Solution :-

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

=> (5)² = (3)² + (AP)²

=> 25 = 9 + (AP)²

=> (AP)² = 25 - 9

=> (AP)² = 16

=> AP = [/tex]\bold\sqrt{16}cm[/tex]

=> AP = 4cm

Now, AB = 2AP (since, OA is bisector)

∴ AB = 2AP = 2 × 4 = 8cm