- #1
samar
- 9
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Hello,
can someone please tell me what's circum-circle?this thing is really confusing me?
can someone please tell me what's circum-circle?this thing is really confusing me?
What Exactly is a Circum-Circle?
- Thread starter samar
- Start date
In summary, a circum-circle is a circle that passes through all the vertices of a triangle. It is also known as the circumcircle or the circumscribed circle. The center of this circle is the intersection of the perpendicular bisectors of the triangle's sides. The radius of the circum-circle is equal to half the length of the triangle's longest side. This geometric concept is often used in geometry and trigonometry to solve problems related to triangles and their properties.
- #2
tiny-tim
Science Advisor
Homework Helper
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Hi samar! 
The circumcircle of a triangle is the unique circle which goes through all three vertices.
Obviously, it is the smallest circle which can contain the whole triangle.
(Not to be confused with the in-circle, or inscribed circle, which is the unique circle whch touches all three sides of the triangle, from the inside, and which is the largest circle which can be contained inside the triangle.!)
For more information, see: http://en.wikipedia.org/wiki/Circumcircle#Circumcircles_of_triangles
The circumcircle of a triangle is the unique circle which goes through all three vertices.
Obviously, it is the smallest circle which can contain the whole triangle.
(Not to be confused with the in-circle, or inscribed circle, which is the unique circle whch touches all three sides of the triangle, from the inside, and which is the largest circle which can be contained inside the triangle.!)
For more information, see: http://en.wikipedia.org/wiki/Circumcircle#Circumcircles_of_triangles
- #3
samar
- 9
- 0
Thanx tiny-tim...your information really helped me ..
thank you once again :)
thank you once again :)
1. What is a circum-circle?
A circum-circle is a circle that passes through all the vertices of a given polygon, including triangles, squares, and other regular or irregular shapes. It is also known as a circumscribed circle.
2. How is a circum-circle different from an inscribed circle?
While a circum-circle passes through the vertices of a polygon, an inscribed circle is tangent to each side of the polygon and is contained inside it. In other words, an inscribed circle is the largest circle that can fit inside a polygon, while a circum-circle is the smallest circle that can encompass a polygon.
3. What is the importance of a circum-circle?
A circum-circle is important in geometry as it provides a way to define and measure the size and shape of polygons. It also helps in identifying and constructing different types of polygons, especially those that are not regular.
4. How is the radius of a circum-circle calculated?
The radius of a circum-circle can be calculated using the formula: R = a / (2*sin(A)), where R is the radius, a is the length of one side of the polygon, and A is the corresponding central angle. Alternatively, the radius can also be calculated using the formula: R = (a*b*c) / (4*√(s*(s-a)*(s-b)*(s-c))), where a, b, and c are the lengths of the sides of a triangle and s is the semi-perimeter.
5. Can a circum-circle exist for all polygons?
No, a circum-circle cannot exist for all polygons. It is only possible for convex polygons, which are polygons with all interior angles less than 180 degrees. Concave polygons, on the other hand, do not have circum-circles as they have at least one interior angle greater than 180 degrees.
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