Question

7. Circle O1 ≅ circle O2. If the radius of circle O1=5cm.

Find the radius of circle O2​

Answer 1

Answer

REF.Image

Since circumference of circle = 2πr

⇒2=2πr

⇒r=1/πcm for both circles

From symmetry, perpendicular AB to

O

1

O

2

also bisects O

1

O

2

As O

1

O

2

=r=

π

1

cm

(O

1

is center for O

1

and O

2

lies on its circumference)

⇒O

1

L=

2

1

×

π

1

=

2π

1

cm

and O

1

A=r=

π

1

cm

⇒ In △O

1

AL, cosθ=

O

1

A

O

1

L

=

2π

1

×π=

2

1

⇒θ=60

∘

=

3

π

As we know angle =

radius

arc

for arc AB of circle C

1

,

arc=2θ×r=2×

3

π

×

π

1

=

3

2

cm

Similarly arc AB of circle C

2

=

3

2

cm

Perimeter of shaded region = AO

1

B+AO

2

B=

3

4

cm

Answer 2

ANSWER : The radius of circle O2 is = 5cm.. Because of the circle O1 and circle O2 is congruent to each other...

Hope, it is helpful for you..