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The radius of a circle which has a 6 cm long chord, 4 cm away from the centre of the circle is
- a)9 cm
- b)8 cm
- c)10 cm
- d)5 cm
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The radius of a circle which has a 6 cm long chord, 4 cm away from the...
In the right triangle OAP,
OA2 = OP2 +AP2 (By Pythagoras theorem)
OA2 = 42 + 32 (perpendicular from the centre of the circle bisects the chord , AP=3cm)
OA2 = 25
OA = 5
Hence the radius of the circle is 5 cm.
Most Upvoted Answer
The radius of a circle which has a 6 cm long chord, 4 cm away from the...
Find the midpoint of the chord. 6/2=3. The midpoint of the chord is 3cm from each point on the chord that touches the circle, and 4 cm from the centre of the circle. Call the distance from the midpoint to the centre m, and half the chord length x. So m=4, and x=3.
-We now have two sides of a right triangle with m and x. Inspection reveals that a line from the centre of the circle to the point where the chord touches the circle is the radius of the circle, and the hypotenuse of a right triangle. Call it r.
r^2=(m^2) + (x^2)= 9+16=25, so the radius is 5cm.
-We now have two sides of a right triangle with m and x. Inspection reveals that a line from the centre of the circle to the point where the chord touches the circle is the radius of the circle, and the hypotenuse of a right triangle. Call it r.
r^2=(m^2) + (x^2)= 9+16=25, so the radius is 5cm.
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Community Answer
The radius of a circle which has a 6 cm long chord, 4 cm away from the...
Understanding the Problem
To find the radius of a circle given a chord and its distance from the center, we can use the properties of circles and right triangles.
Given Information
- Length of the chord = 6 cm
- Distance from the center to the chord = 4 cm
Visualizing the Circle
1. Draw the Circle: Start by sketching the circle with the center O.
2. Mark the Chord: Draw the chord AB, which is 6 cm long.
3. Identify the Midpoint: Let M be the midpoint of the chord AB. Thus, AM = MB = 3 cm.
Using Right Triangle Properties
- Drop a Perpendicular: From the center O, draw a perpendicular line to the chord AB, meeting at M. This line represents the distance from the center to the chord, which is given as 4 cm.
- Forming the Right Triangle: Triangle OMA is a right triangle where:
- OM = 4 cm (perpendicular distance)
- AM = 3 cm (half the length of the chord)
Applying the Pythagorean Theorem
- Finding the Radius: In right triangle OMA, the radius OA can be found using:
- OA² = OM² + AM²
- OA² = 4² + 3²
- OA² = 16 + 9
- OA² = 25
- OA = √25 = 5 cm
Conclusion
- Therefore, the radius of the circle is 5 cm.
- The correct answer is option D.
To find the radius of a circle given a chord and its distance from the center, we can use the properties of circles and right triangles.
Given Information
- Length of the chord = 6 cm
- Distance from the center to the chord = 4 cm
Visualizing the Circle
1. Draw the Circle: Start by sketching the circle with the center O.
2. Mark the Chord: Draw the chord AB, which is 6 cm long.
3. Identify the Midpoint: Let M be the midpoint of the chord AB. Thus, AM = MB = 3 cm.
Using Right Triangle Properties
- Drop a Perpendicular: From the center O, draw a perpendicular line to the chord AB, meeting at M. This line represents the distance from the center to the chord, which is given as 4 cm.
- Forming the Right Triangle: Triangle OMA is a right triangle where:
- OM = 4 cm (perpendicular distance)
- AM = 3 cm (half the length of the chord)
Applying the Pythagorean Theorem
- Finding the Radius: In right triangle OMA, the radius OA can be found using:
- OA² = OM² + AM²
- OA² = 4² + 3²
- OA² = 16 + 9
- OA² = 25
- OA = √25 = 5 cm
Conclusion
- Therefore, the radius of the circle is 5 cm.
- The correct answer is option D.
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The radius of a circle which has a 6 cm long chord, 4 cm away from the centre of the circle isa)9 cmb)8 cmc)10 cmd)5 cmCorrect answer is option 'D'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The radius of a circle which has a 6 cm long chord, 4 cm away from the centre of the circle isa)9 cmb)8 cmc)10 cmd)5 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radius of a circle which has a 6 cm long chord, 4 cm away from the centre of the circle isa)9 cmb)8 cmc)10 cmd)5 cmCorrect answer is option 'D'. Can you explain this answer?.
The radius of a circle which has a 6 cm long chord, 4 cm away from the centre of the circle isa)9 cmb)8 cmc)10 cmd)5 cmCorrect answer is option 'D'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The radius of a circle which has a 6 cm long chord, 4 cm away from the centre of the circle isa)9 cmb)8 cmc)10 cmd)5 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radius of a circle which has a 6 cm long chord, 4 cm away from the centre of the circle isa)9 cmb)8 cmc)10 cmd)5 cmCorrect answer is option 'D'. Can you explain this answer?.
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