Question

O is the center of two concentric circles with radii of bigger and smaller circle are 10 cm and r cm respectively. AB is the chord of the bigger circle such that it touches the smaller circle at point P. Length of the chord is 16 cm. Find the r.

Answer 1

Step-by-step explanation:

Let C1,C2 be two circles of radius 10,6 respectively.

Let r1=10 cm and r2=6 cm

Draw a chord AB tangent to C2 at point P.

Join O−A and O−B

OP=6 cm ....... (Radius of smaller circle)

OA=OB=10 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=102−62=100−36=64

∴AP=8 cm

Similarly, PB=8 cm

∴ AB=AP+PB=8+8=16 cm

Hence, the answer is 16.

Answer 2

Step-by-step explanation:

Let C

1

,C

2

be two circles of radius 10,6 respectively.

Let r

1

=10 cm and r

2

=6 cm

Draw a chord AB tangent to C

2

at point P.

Join O−A and O−B

OP=6 cm ....... (Radius of smaller circle)

OA=OB=10 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

=10

2

−6

2

=100−36=64

∴AP=8 cm

Similarly, PB=8 cm

∴ AB=AP+PB=8+8=16 cm

Hence, the answer is 16.