Question

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

Answer 1

draw 2 concentric circles and draw a tangent touching smaller circle being chord of larger circle then by pythagoras theorm calculate side and multiply it by 2 to get the kength of chord

Answer 2

Let two circles have the same centre O and AB is a chord of the larger circle touching the smaller circle at C.

OA=5cm and OC=3cm

Now,

As we know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Therefore,

In △OAC,

OA²=OC²+AC² (By pythagoras theorem)

⇒AC²=OA²−OC²

⇒AC²=(5)²−(3)²

$⇒AC= \sqrt{25 - 9} = \sqrt{16} = 4cm$

Since perpendicular drawn from the centre of circle bisects the chord.

Therefore,

AB=2AC

⇒AB=2×4=8cm

Hence the length of the chord is 8cm.