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?
Question:
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?
Answer:
Let's think step by step.

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\frac{1}{2}
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?
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