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In two circles arc of same length substended angles 30°&60°at the centre. Find the ratio of the radii?
Most Upvoted Answer
In two circles arc of same length substended angles 30°&60°at the cent...
Given Data:
- Two circles with arcs of the same length
- Subtended angles at the center are 30° and 60°
Ratio of the Radii:
To find the ratio of the radii of the two circles, we can use the formula:
\[ \text{Arc Length} = 2\pi r \left( \frac{\text{Angle}}{360} \right) \]
Given that the arc length is the same for both circles, we can set up the following equation:
\[ 2\pi r_1 \left( \frac{30}{360} \right) = 2\pi r_2 \left( \frac{60}{360} \right) \]
Simplifying the above equation, we get:
\[ r_1 = 2r_2 \]
Therefore, the ratio of the radii of the two circles is 2:1.
This means that the radius of the first circle is twice the radius of the second circle.
Explanation:
- Two circles with the same arc length will have different central angles depending on their radii.
- The formula for calculating arc length is used to set up an equation to find the ratio of the radii.
- By simplifying the equation, we find that the radius of the first circle is twice the radius of the second circle.
- Hence, the ratio of the radii of the two circles is 2:1.
- Two circles with arcs of the same length
- Subtended angles at the center are 30° and 60°
Ratio of the Radii:
To find the ratio of the radii of the two circles, we can use the formula:
\[ \text{Arc Length} = 2\pi r \left( \frac{\text{Angle}}{360} \right) \]
Given that the arc length is the same for both circles, we can set up the following equation:
\[ 2\pi r_1 \left( \frac{30}{360} \right) = 2\pi r_2 \left( \frac{60}{360} \right) \]
Simplifying the above equation, we get:
\[ r_1 = 2r_2 \]
Therefore, the ratio of the radii of the two circles is 2:1.
This means that the radius of the first circle is twice the radius of the second circle.
Explanation:
- Two circles with the same arc length will have different central angles depending on their radii.
- The formula for calculating arc length is used to set up an equation to find the ratio of the radii.
- By simplifying the equation, we find that the radius of the first circle is twice the radius of the second circle.
- Hence, the ratio of the radii of the two circles is 2:1.
Community Answer
In two circles arc of same length substended angles 30°&60°at the cent...
Given Information:
- Two circles with arcs of the same length
- Subtended angles at the center are 30° and 60°
Formula to Find the Ratio of Radii:
- The ratio of the radii of two circles with arcs of the same length and subtended angles at the center can be found using the formula:
Ratio of Radii = (Angle of Circle 1) / (Angle of Circle 2)
Calculation:
- In this case, the angles subtended at the center are 30° and 60°.
- Therefore, the ratio of the radii of the two circles is:
Ratio of Radii = 30° / 60°
Ratio of Radii = 1/2
Conclusion:
- The ratio of the radii of the two circles is 1:2.
- Two circles with arcs of the same length
- Subtended angles at the center are 30° and 60°
Formula to Find the Ratio of Radii:
- The ratio of the radii of two circles with arcs of the same length and subtended angles at the center can be found using the formula:
Ratio of Radii = (Angle of Circle 1) / (Angle of Circle 2)
Calculation:
- In this case, the angles subtended at the center are 30° and 60°.
- Therefore, the ratio of the radii of the two circles is:
Ratio of Radii = 30° / 60°
Ratio of Radii = 1/2
Conclusion:
- The ratio of the radii of the two circles is 1:2.
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In two circles arc of same length substended angles 30°&60°at the centre. Find the ratio of the radii?
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In two circles arc of same length substended angles 30°&60°at the centre. Find the ratio of the radii? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In two circles arc of same length substended angles 30°&60°at the centre. Find the ratio of the radii? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In two circles arc of same length substended angles 30°&60°at the centre. Find the ratio of the radii?.
In two circles arc of same length substended angles 30°&60°at the centre. Find the ratio of the radii? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In two circles arc of same length substended angles 30°&60°at the centre. Find the ratio of the radii? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In two circles arc of same length substended angles 30°&60°at the centre. Find the ratio of the radii?.
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