Math, asked by manjindersingh7583, 8 months ago

if in two circles arcs of the same length subtend angles of 45 degree and 90 degree at the centre find the ratio of their radii
plz answer

Answers

Answered by Anonymous

To find :

we need to find the ratio of radii of circles.

Solution :

Length of arcs of both circles are equal
Angles subtended at centre of both circles are 45° and 90°

Let length of two circles be l

Angles subtended at centre are

45° = 45 × π/180 radian

45 ° = π/4 radian

90° = 90 × π/180 radian

90° = π/2 radian

We know that,

theta = length of arc/radius of circle

And

$\boxed{ \bf \: r = \frac{l}{ \theta} }$

Let the radius of two circles be r1 and r2

Radius of 1st circle =

$r_1 = \large \rm \: \frac{ \frac{l}{\pi} }{4}$

R1 = l × 4/π

R1 = 4l/π ....1)

Radius of 2nd circle

R2 = l/π/2

R2 = l × 2/π

R2 = 2l/π ...2)

Now,

Ratio of Radii of two circles

= 4l/π/2l/π

= 4l/π × π/2l

= 4l/2l

= 2/1

Hence,

Ratio of radii of two circles is 2 : 1 .

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Answered by k047

Let r1 and r2 be the radii of the two circles. Then,

θ1=60∘=(60×π180)c=(π3)c

and θ2=75∘=(75×π180)c=(5π12)c.

Let the length of each arcbe lcm. Then,

l=r1θ1=r2θ2.

⇒(r1×π3)=(r2=5π12)

⇒=r1r2=54.

Hence, r1:r2=5:4.

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if in two circles arcs of the same length subtend angles of 45 degree and 90 degree at the centre find the ratio of their radii plz answer ​

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To find :

Solution :

if in two circles arcs of the same length subtend angles of 45 degree and 90 degree at the centre find the ratio of their radii
plz answer