# Circumcircle of a triangle.

1. Feb 8, 2005

### primarygun

For a triangle, 3 sides are given.
What's the radius of its circumcircle?
Are we able to get it without using cosine law or sine law or heron formula?

2. Feb 8, 2005

### CollectiveRocker

What is a circumcircle?

3. Feb 8, 2005

### primarygun

An outern circle .

4. Feb 8, 2005

### CollectiveRocker

I'm really sorry, but I have no idea what you are talking about.

5. Feb 8, 2005

### primarygun

A circle surrounds a triangle, the three vertexs of the triangle touches the circumference

6. Feb 8, 2005

### CollectiveRocker

Oh, I apologize. The only way which I know of to get that is with the law of cosines.

7. Feb 8, 2005

### primarygun

My teachers haven't taught us the cosine law, but this question is in the part of properties of circle. Moreover, he hasn't taught heron formula.

8. Feb 9, 2005

### Staff: Mentor

9. Feb 10, 2005

### VietDao29

Hi,
First, use the law of cosine:
$$a^{2} = b^{2} + c^{2} - 2bc\cos{A}$$
$$b^{2} = a^{2} + c^{2} - 2ac\cos{B}$$
$$c^{2} = a^{2} + b^{2} - 2ab\cos{C}$$
to find out cos of one of the angle in the triangle, then use $sin^{2}\theta + cos^{2}\theta = 1$ (In a triangle, $sin\theta$ is always positive) to find its sine and then use the law of sine to find out the radius of the circumcircle.
The law of sine is:
$$\frac{a}{\sin{A}} = \frac{b}{\sin{B}} = \frac{c}{\sin{C}} = 2 \times R$$
Where R is the radius of the circumcircle.
Hope you get it.
Viet Dao,

10. Feb 11, 2005

### primarygun

No need sin law.
I know many methods, but currently I want the most simpliest one.
Anyway, thank you. :P