First we construct a small circle inside
a larger circle. Then a third circle the same size as the interior
circle is constructed as seen below.
Now we will construct the perpendicular
bisector of the line connecting the center of the first interior
circle and a point on the small circle . Then the center of the
new circle is the intersection of the perpendicular line and the
first line through the center of the large circle.
Now an isosoceles triangle is formed
After animating the small circles ,
all of my resulting triangles were isosceles. here is one example.
This was a very challenging problem