SOLUTION: How long are the sides of an equilateral triangle inside a one inch circle?

Draw three green radii (which are 1 inch long) to the vertices, label 
the center of the circle O.



Extend AO down to intersect BC at point D



Triangle BDO is a 30°-60°-90° right triangle.
Therefore the red line OD is one half of green radius OB

So OB is 1 inch, and OD is  inch, so by the Pythagorean
theorem:

BD² + OD² = OB²

BD² + ()² = (1)²

BD² +  = 1

BD² = 

BD = 

BD = 

BD is one-half of BC, a side of eqilateral triangle ABC.

Therefore BC is 

So each side of the equilateral triangle is  inches.

Edwin