A circle is inscribed within a quarter circle. A line of length 1 extends from the vertical edge to the arc of the quarter circle is parallel to the horizontal edge of the quarter circle, and tangent to the inscribed circle.
What is the radius, R, of the quarter circle?
1 point for a numerical solution, 2 points for an exact solution using nested square roots, 3 points for finding a quartic polynomial whose real positive solution is R.