Circumscribed Circle Triangle

Introduction

In geometry, a circle passing through all the vertex of a polygon is called as circumscribed circle. So, the circle passing through all the vertex of a triangle is called as the circumscribed circle of the triangle. Also, the triangle is called as cyclic triangle.

The center of the circumscribed circle is called as the circumcenter. The circumscribed circle of a triangle can be drawn using the perpendicular bisectors of a triangle.
Construction of Circumscribed Circle of a Triangle

Here we are going to learn how to draw a circumscribed circle of a triangle using perpendicular bisectors.

1. Draw a triangle ABC with vertices A, B, and C of any dimensions.

circumscribed circle triangle

 

 

 

 

 

circumscribed circle triangle

 

 

2. Now we have to draw perpendicular bisector to the side AB.

From vertex A, using a compass with width more than half of the length of the side AB, draw two arcs on each side of line segment AB. Without changing the compass reading draw another two arcs on both sides of the line segment AB from vertex B. Join the points of intersection between the arcs. The line is the perpendicular bisector of side AB.

circumscribed circle triangle

 

 

 

 

circumscribed circle triangle

3. Now we have to draw the perpendicular bisector of side BC. Draw the perpendicular bisector for the side BC using the same procedure.

 

 

 

circumscribed circle triangle

 

 

 

circumscribed circle triangle

4. Mark the point of intersection between the perpendicular bisectors of sides AB and BC as O. Now, the point O is the circumcenter of triangle ABC.

 

 

circumscribed circle triangle

 

 

 

 

circumscribed circle triangle

5. Adjust the compass width from point O to one of the vertex of the triangle. Using it as radius, draw a circle around the point O (Circumcenter). The circle passes through all the vertices of the triangle, and it is the circumscribed circle of the triangle ABC. The radius of the circle is OA or OB or OC. And the triangle ABC is called as cyclic triangle.

 

 

circumscribed circle triangle

 

 

 

 

 

circumscribed circle triangle