Question

If in tow circles arcs of the same length subtend angles
60^०and70^०at the center,find the ration of their radios
​

Answer 1

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Q//. If in two circles arcs of the same length subtend angles 60° and 70° at the center, find the ratio of their radii?

$\LARGE{ \underline{\underline{ \orange{ \sf{Required \: answer:}}}}}$

GiveN:

• The angle subtended by arcs is 60° and 70°
• The length of arcs are same.

To FinD:

• Ratio of the radius?

Step-by-step Explanation:

Let l be the length of the arcs of two circles.

And r be the radius of circle 1 and R be the radius of circle 2. We know that,

• l = r$\theta$

$\theta$ is the angle subtended by the arcs in the centre. Then,

1. l = r × 60°
2. l = R × 70°

The length of the arcs is same. So,

⇒ r × 60° = R × 70°

⇒ r/R = 70°/ 60°

⇒ r/R = 7/6

The ratio of the radius of the two circles is 7 : 6 (Ans)

Answer 2

Answer:

Question:-

If in two circles arcs of the same length subtend angles 60° and 70° at the centre, find the ratio of their radios.

Given:-

• The angle subtended by arcs is 60° and 70°.

• The length of arcs are same.

To find:-

• Ratio of the radius?

Step-by-step explanation:-

Let I be the length of the arcs of two circles.

And r be the radius of circle 1 and R be the radius of circle 2. We know that,

• l = r0

0 is the angle subtented by the arcs in the same centre. Then,

1. l = r×60°

2. l = R×70°

The length of the arcs is same. So,

=> r×60° = R×70°

=> r/R = 70°/60°

=> r/R = 7/6

Therefore, the ratio of the radius of the two circles is 7:6.