Class 9 Exam > Class 9 Questions > Which of the following statements is true con...
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Which of the following statements is true concerning inscribed and circumscribed circles?
- a)Both circles are identical in size
- b)An inscribed circle touches all vertices of a polygon
- c)An inscribed circle cannot exist within a polygon
- d)A circumscribed circle is always larger than the inscribed circle
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Which of the following statements is true concerning inscribed and cir...
An inscribed circle touches all sides of a polygon, while a circumscribed circle passes through all vertices of the polygon. This distinction is vital in triangle geometry and other polygons, providing insight into their properties and relationships.
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Which of the following statements is true concerning inscribed and cir...
Understanding Circles in Polygons
When discussing inscribed and circumscribed circles, it's crucial to understand their definitions and properties.
Inscribed Circle
- An inscribed circle (or incircle) is a circle that is tangent to all sides of a polygon.
- It exists only in polygons that are tangential, meaning their sides can touch a single circle.
Circumscribed Circle
- A circumscribed circle (or circumcircle) is a circle that passes through all vertices of a polygon.
- It encompasses the entire polygon and is defined by its vertices.
Key Relationship between the Two Circles
- The circumradius (radius of the circumscribed circle) is always greater than or equal to the inradius (radius of the inscribed circle) for any polygon.
- This is because the circumcircle must extend to the vertices, while the incircle fits snugly within the polygon.
Why Option D is Correct
- The statement "A circumscribed circle is always larger than the inscribed circle" is true because:
- The circumcircle surrounds the polygon, while the incircle is contained within it.
- In most cases (except for certain degenerate cases), the circumradius will be larger than the inradius.
Conclusion
- In summary, the relationship between the inscribed and circumscribed circles illustrates fundamental geometric principles, confirming that option 'D' is indeed correct.
When discussing inscribed and circumscribed circles, it's crucial to understand their definitions and properties.
Inscribed Circle
- An inscribed circle (or incircle) is a circle that is tangent to all sides of a polygon.
- It exists only in polygons that are tangential, meaning their sides can touch a single circle.
Circumscribed Circle
- A circumscribed circle (or circumcircle) is a circle that passes through all vertices of a polygon.
- It encompasses the entire polygon and is defined by its vertices.
Key Relationship between the Two Circles
- The circumradius (radius of the circumscribed circle) is always greater than or equal to the inradius (radius of the inscribed circle) for any polygon.
- This is because the circumcircle must extend to the vertices, while the incircle fits snugly within the polygon.
Why Option D is Correct
- The statement "A circumscribed circle is always larger than the inscribed circle" is true because:
- The circumcircle surrounds the polygon, while the incircle is contained within it.
- In most cases (except for certain degenerate cases), the circumradius will be larger than the inradius.
Conclusion
- In summary, the relationship between the inscribed and circumscribed circles illustrates fundamental geometric principles, confirming that option 'D' is indeed correct.
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Which of the following statements is true concerning inscribed and circumscribed circles?a)Both circles are identical in sizeb)An inscribed circle touches all vertices of a polygonc)An inscribed circle cannot exist within a polygond)A circumscribed circle is always larger than the inscribed circleCorrect 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 Which of the following statements is true concerning inscribed and circumscribed circles?a)Both circles are identical in sizeb)An inscribed circle touches all vertices of a polygonc)An inscribed circle cannot exist within a polygond)A circumscribed circle is always larger than the inscribed circleCorrect 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 Which of the following statements is true concerning inscribed and circumscribed circles?a)Both circles are identical in sizeb)An inscribed circle touches all vertices of a polygonc)An inscribed circle cannot exist within a polygond)A circumscribed circle is always larger than the inscribed circleCorrect answer is option 'D'. Can you explain this answer?.
Which of the following statements is true concerning inscribed and circumscribed circles?a)Both circles are identical in sizeb)An inscribed circle touches all vertices of a polygonc)An inscribed circle cannot exist within a polygond)A circumscribed circle is always larger than the inscribed circleCorrect 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 Which of the following statements is true concerning inscribed and circumscribed circles?a)Both circles are identical in sizeb)An inscribed circle touches all vertices of a polygonc)An inscribed circle cannot exist within a polygond)A circumscribed circle is always larger than the inscribed circleCorrect 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 Which of the following statements is true concerning inscribed and circumscribed circles?a)Both circles are identical in sizeb)An inscribed circle touches all vertices of a polygonc)An inscribed circle cannot exist within a polygond)A circumscribed circle is always larger than the inscribed circleCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Which of the following statements is true concerning inscribed and circumscribed circles?a)Both circles are identical in sizeb)An inscribed circle touches all vertices of a polygonc)An inscribed circle cannot exist within a polygond)A circumscribed circle is always larger than the inscribed circleCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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Which of the following statements is true concerning inscribed and circumscribed circles?a)Both circles are identical in sizeb)An inscribed circle touches all vertices of a polygonc)An inscribed circle cannot exist within a polygond)A circumscribed circle is always larger than the inscribed circleCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Which of the following statements is true concerning inscribed and circumscribed circles?a)Both circles are identical in sizeb)An inscribed circle touches all vertices of a polygonc)An inscribed circle cannot exist within a polygond)A circumscribed circle is always larger than the inscribed circleCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Which of the following statements is true concerning inscribed and circumscribed circles?a)Both circles are identical in sizeb)An inscribed circle touches all vertices of a polygonc)An inscribed circle cannot exist within a polygond)A circumscribed circle is always larger than the inscribed circleCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Which of the following statements is true concerning inscribed and circumscribed circles?a)Both circles are identical in sizeb)An inscribed circle touches all vertices of a polygonc)An inscribed circle cannot exist within a polygond)A circumscribed circle is always larger than the inscribed circleCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 9 tests.
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