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.

Answer 1

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Asked on December 26, 2019 byNandha 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 C1,C2 be two circles of radius 13,12 respectively.

Let r1=13 cm and r2=12 cm

Draw a chord AB tangent to C2 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 C2 and OP perpendicular AB

∴ ∠OPA=∠OPB=90o

Using Pythagoras theorem,

OA2=OP2+AP2

⟹AP2=OA2−OP2

⟹AP2=132−122=169−144=25

∴AP=5 cm

Similarly, PB=5 cm

∴ 

Step-by-step explanation:

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Answer 2

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.