Skip Navigation Links
   
Circumcenter
To enroll in any of our courses, click here
 
   
Circumcenter

The circumcircle of a triangle is a circle which passes through all the vertices of the triangle. The center of this circle is called the circumcenter and it is equidistant from the three vertices of the triangle.
People who saw this lesson also found the
following lessons useful:
Rational Expression
Trigonometric Ratio: Example
Circle: Chord
Circle: Tangent
Systems of Simultaneous Linear Equations
Example: Find the coordinates of the circumcentre of the triangle whose vertices are (6, 4), (6, -2) and (2, -2). Also, find its circum-radius.
Solution: Recall that the circumcentre of a triangle is equidistant from the vertices of a triangle. Let A (6, 4), B (6, -2) and C (2, -2) be the vertices of the given triangle and let P(x, y) be the circumcentre of this triangle. Then,
PA = PB = PC
PA2 = PB2 = PC2
Now, PA2 = PB2
(x - 6)2 + (y - 4)2 = (x - 6)2 + (y + 2)2
x2 + y2 - 12x - 8y + 52 = x2 + y2 - 12x + 4y + 40
12y = 12
y = 1
and, PB2 - PC2
(x - 6)2 + (y + 2)2 = (x - 2)2 + (y + 2)2
x2 + y2 - 12x + 4y + 40 = x2 + y2 - 4x + 4y + 8
8x = 32
x = 4
So, the coordinates of the circumcentre P are (4, 1). Also, Circum-radius = PA = PB = PC = ((4 - 6)2 + (1 - 4)2) = 13.
 
   
As many of you know, Winpossible's online courses use a unique teaching method where an instructor explains the concepts in any given area to you in his/her own voice and handwriting, just like you see your teacher explain things to you on a blackboard in your classroom. All our courses include teacher's instruction, practice questions as well as end-of-lesson quizzes for practice. You can enroll in any of our online courses by clicking here.

The format of Winpossible's online courses is also very suitable for teachers who are using an interactive whiteboard such as Smartboard on Promethean in their classrooms, because the course lessons can be easily displayed on such interactive whiteboards. Volume pricing is available for schools interested in our online courses. For more information, please contact us at educators@winpossible.com.

 
       
     
 Copyright © Winpossible, 2010 - 2011
Best viewed in 1024x768 & IE 5.0 or later version
l> l>