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. 

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