Question

two concentric circles are the radii 13cm and 15cm , the length of the chord of a larger circle which touches the smaller circle is ​

Answer 1

Answer:

24cm

Step-by-step explanation:

Given−

O is the centre of two concentric circles.

The radius of the outer circle=OQ=r1 =13cm

The radius of the inner circle=r2  =5cm.

A chord AB of the outer circle touches the inner  one at P.

To find out−

The length of AB

Solution−

We join OA&OP.

∴OA=r2 & OP=r1

Now OP⊥AB i.e OP⊥AP since the radius through the point of contact of tangent to a circle is perpendicular to the tangent.

∴ΔOAP is aright one with OA as hypotenuse.

So, applying Pythagoras theorem, we get

AP=under root OA ^2−OP^2=under root13^2cm-5^2cm=12cm

Again AB=2×AP=2×12cm=24cm

since the perpendicular from the center of a circle to any of its chord bisects the latter.

∴The length of AB=24cm.

HOPE IT HELPS!!