Question

Two concentric circles are of radii 13 cm and 5 cm. Find the length of the chord of the larger circle which touches the

smaller circle at a point.​

Answer 1

Step-by-step explanation:

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+AC

(By pythagoras theorem)

⇒AC²=OC²-OA²

AC²= 5²-3²

Ac =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