Given that in a triangle ABC, AB = 2cm, AC = 3cm, Find the radius of the circumscibed circle of ABC.
We know that the three vertices of the triangle lie on a circle. If we say that point A is the origin (0, 0), then we could say that since the length AC is 3 cm, the co-ordinate of C is (3, 0).
We know that point B lies 2cm from point A making an angle of .
The vertical position of point B can be found by
and the horizontal position of point B can be found by
So point B is at .
Now that you have three points that lie on your circle, you can substitute them into the general equation for a circle and solve them simultaneously for (you are trying to find r).
You can find BC either by using law of cosines or by constructing an altitude from point B and using 30-60-90 triangles. Either way, you should get .
There is a formula for the area of a triangle, , where R is the circumradius. We know AB, BC, CA, and just need to find the area. This is easy, since
Hence,
.