# Parabolic Circle

Geometry Level 4

Consider the parabola $$y=ax^2 + bx+c$$, if it intersects $$x$$-axis at $$\alpha > 0$$ and $$\beta > 0$$, find the length of the tangent from the origin to the circle passing through $$\alpha$$ and $$\beta$$ when $$a=2, b>120, c=162$$. Hint: consider$$\alpha$$ and $$\beta$$ to be diametric end points.

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