Question

The radius of a circle is 9 cm. Find the
length of an arc of this circle which
cuts off a chord of length, equal to
length of radius.
​

Answer 1

Answer:

OA=9cm=OB=OC

CB=9cm

Given,

chord CB=9cm

radii OC=OB=9cm

∠COB=60

o

(as triangle is an equilateral triangle)

so, length of arc CB=(

360

o

sectorangle

)×2πr

=

360

o

60

o

×2π×9

=

6

18π

=3πcm.

Answer 2

Formula to find arc length:

   Arc length = 2πr (θ / 360°),

where r is the radius of the circle and θ is the central angle in degree.

Drawing a figure:

   Before we solve the problem, we draw a circle with centre A. We draw two radius in such a way that their circumferential ends can be joined in same distance as of radius's length. We draw two end points B, C. Joining A, B, C, we get a triangle ABC which is an equilateral triangle, making an angle ∠BAC = 60° at the centre and BC is the chord mentioned in the question.

Solution:

We have to find the arc length of BC.

Here radius of the circle, r = 9 cm,

central angle, θ = 60°

Hence, arc length of BC is

= 2πr (θ/360°)

= 2π (9) * (60° / 360°) c

= 2 * (22/7) * 9 * (1/6) cm

= 9.43 cm