CIRCUMCIRCLE
Definition Of Circumcircle
A circle that passes through all of the vertices of a polygon is called a Circumcircle or Circumscribed circle.
More About Circumcircle
The center of the circumcircle is called the circumcenter.
All triangles, rectangles, and regular polygons have circumcircles.
Video Examples: Construction of circumcircle of a triangle
Example of Circumcircle
In the figure below, the circumcircle (in black) of the triangle ABC passes through all its vertices A, B, and C
Solved Example on Circumcircle
Ques: Which of the following figure shows the circumcircle of the triangle?
Choices:
A. Figure 1
B. Figure 2
C. Figure 3
D. Figure 4
Correct Answer: C
Solution:
Step 1: A circle that passes through all of the vertices of a triangle is called circumcircle of a triangle.
Step 2: In Figure 3, the circle passes through all the vertices of the triangle ABC.
Step 3: So, Figure 3 is the circumcircle of the triangle.
Quick Summary
- A circumcircle passes through all vertices of a polygon.
- The center of the circumcircle is the circumcenter.
- Triangles, rectangles, and regular polygons have circumcircles.
🍎 Teacher Insights
Use dynamic geometry software to demonstrate the construction of circumcircles for various polygons. Emphasize the relationship between the circumcenter and the perpendicular bisectors of the polygon's sides.🎓 Prerequisites
- Circles
- Polygons
- Triangles
- Vertices
Check Your Knowledge
Q1: Which of the following is true about a circumcircle?
Frequently Asked Questions
Q: What is the circumcenter?
A: The circumcenter is the center of the circumcircle. It is the point of intersection of the perpendicular bisectors of the sides of the polygon.
Q: Do all polygons have circumcircles?
A: No, only certain polygons such as triangles, rectangles, and regular polygons have circumcircles.