Use complete sentences to answer the questions.

Part 1: What is the circumcenter of a triangle?
Part 2: Where is the circumcenter located in relation to the triangle?

Question

Use complete sentences to answer the questions.
 
Part 1: What is the circumcenter of a triangle? 
Part 2: Where is the circumcenter located in relation to the triangle?

anonymous · Answer

1. - sorry but i'm not sure that i think it correct but how i remember if you make (sign) the bisectors  lines of degrees of this triangle so where those will have the intersect point - so there - this will be the circumcenter of a triangle 
2. The circumcenter is the point where the distance from this point to any of the triangle’s sides is constant.

anonymous · Answer

why did you just copy & paste that? lol

anonymous · Answer

Hmm. I did not. I used my own writings, because I am across. But I changed my name not too long ago. Sorry for the confusion but do you understand it or would you like me to elaborate?

anonymous · Answer

The circumcircle always passes through all three vertices of a triangle. Its center is at the point where all the perpendicular bisectors of the triangle's sides meet. This center is called the circumcenter.

The radius of the circumcircle is also called the triangle's circumradius.
For right triangles
In the case of a right triangle, the hypotenuse is a diameter of the circumcircle, and its center is exactly at the midpoint of the hypotenuse. This is the same situation as Thales Theorem, where the diameter subtends a right angle to any point on a circle's circumference. 

If you drag the triangle in the figure above you can create this same situation.
For equilateral triangles
In the case of an equilateral triangle, where all three sides (a,b,c) are have the same length, the radius of the circumcircle is given by the formula:

  Calculator
where s is the length of a side of the triangle.
If you know all three sides
If you know the length (a,b,c) of the three sides of a triangle, the radius of its circumcircle is given by the formula:
	  Calculator
If you know one side and its opposite angle
The diameter of the circumcircle is given by the formula:

  Calculator
where a is the length of one side, and A is the angle opposite that side.
This gives the diameter, so the radus is half of that

This is derived from the Law of Sines.

anonymous · Answer

Which flvs lesson is this? i am also an flvs student