On 20 Jul, 14:47, Richard wrote:
Given an equilateral triangle of side 185 mm, how do I calculate the
diameter or radius of the circle that intersects with the three corners
of the triangle?

My Zeus tables explain how to set up a drilling rig for a given
diameter, but not the reverse.

The formula would be helpful.

A link to a web site of such useful information would be wonderful!

TIA

Richard

If the equilateral triangle is converted into three equal sized
triangles within the main one, using the centre of the circle as the
common point where all three converge, you get three triangles with
two 30deg angles and one of 120deg, and the lines from the side of the
circle to the centre is the radius of the circle.

Half one of these triangle, you get a right angled triangle with a
30deg and 60 deg angles. Using trig, the 185mm triangle edge now = 2
x the (A)djacent side of the triangle in relation to the 30deg angle.

Formula is therefore (185/2) / cos(30) = 106.80. As a generic
formula, r = L/2 / cos(30).

http://www.google.co.uk/search?hl=en...grees%29&meta=

I'm sure there is a simpler way, but that was an enjoyable challenge
to me as someone who hadn't done any trig in about 20 years!!

Matt