Question

2. Two concentric circle of radius a and b (a>vb) are given. Find the length
of the chord of the largest ciode which touches the graller
corcle​

Answer 1

Answer:

Let C

1

,C

2

be two circles of radius a,b respectively.

Chord AB tangent to C

2

at point C.

Join O−B

OA=a=OB,OC=b

AB is tangent to C

2

and OC perpendicular AB

∴ ∠OCA=90

o

Using Pythagoras theorem,

OA

2

=OC

2

+AC

2

⟹AC

2

=OA

2

−OC

2

⟹AC=

a

2

−b

2

Similarly, BC=

a

2

−b

2

∴ AB=AC+CB=

a

2

−b

2

+

a

2

−b

2

Hence, AB=2

a

2

−b

2

.