A circle rests in the interior of the parabola with equation $y=x^2$ so that it is tangent to the parabola at two points. How much higher is the center of the circle than the points of tangency ?
I've seen the solution of the problem here on Aops site and it left me a bit skeptical.
I am not referring to the validity of the solution,which is correct, but rather to the fact that the problem has been solved using basic calculus.
Now, I came across this problem on Aops 2 volume book which doesn't teach any calculus,so it's clear that there's a simpler solution to the problem that relies only on basic geometry;however I've not been able to find it...
So I am asking if someone knows a solution which involves only basic geometry.