Given that in a triangle ABC, AB = 2cm, AC = 3cm, Find the radius of the circumscibed circle of ABC.

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- Aug 4th 2012, 03:06 AMshiny718Find the radius of the circumscribed circle
Given that in a triangle ABC, AB = 2cm, AC = 3cm, Find the radius of the circumscibed circle of ABC.

- Aug 4th 2012, 03:19 AMProve ItRe: Find the radius of the circumscribed circle
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). - Aug 4th 2012, 09:21 AMrichard1234Re: Find the radius of the circumscribed circle
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,

.