Circumcentre of an equilateral triangle

[Chronos000]

1. Homework Statement [

what is the distance from one corner of an equilateral triangle of sides a to the circumcentre?


I can figure out the length from one corner to the opposite side to be sqrt3*a/2 but that's about it. I just can't see how to do this.

thanks

 

[Dick]

Drop a perpendicular from the circumcenter to a side. That gives you a 30-60-90 triangle whose hypotenuse is the radius you are looking for.

 

[Chronos000]

thanks, the answer is a/sqrt3, I thought there was some way to do this without cos or sin but perhaps not

 

[Dick]

thanks, the answer is a/sqrt3, I thought there was some way to do this without cos or sin but perhaps not

You could just use the pythagorean theorem if you really want to. If you call the circumcircle radius r, then the a*sqrt(3)/2 distance you computed minus r is the shorter leg of your 30-60-90 triangle. Now use the pythagorean theorem on it to solve for r. You don't really NEED the trig.