Question

Two concentric circles of radii 15 cm, 12 cm are drawn. Find the length of chord of larger circle which touches the smaller circle.

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Asked on December 26, 2019 by

Nandha Kandwal

Two concentric circles are of radii 13 cm and 12 cm. What is the length (in cm) of the chord of the larger circle which touches the smaller circle?

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ANSWER

Let C

1

,C

2

be two circles of radius 13,12 respectively.

Let r

1

=13 cm and r

2

=12 cm

Draw a chord AB tangent to C

2

at point P.

Join O−A and O−B

OP=12 cm ....... (Radius of smaller circle)

OA=OB=13 cm ....... (Radius of bigger circle)

AB is tangent to C

2

and OP perpendicular AB

∴ ∠OPA=∠OPB=90

o

Using Pythagoras theorem,

OA

2

=OP

2

+AP

2

⟹AP

2

=OA

2

−OP

2

⟹AP

2

=13

2

−12

2

=169−144=25

∴AP=5 cm

Similarly, PB=5 cm

∴ AB=AP+PB=5+5=10 cm

Hence, the answer is 10.