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Math Prize 2021 Problem 12

Source:

September 19, 2021
conicsparabolaMath Prize for Girls

Problem Statement

Let P1P_1, P2P_2, P3P_3, P4P_4, P5P_5, and P6P_6 be six parabolas in the plane, each congruent to the parabola y=x2/16y = x^2/16. The vertices of the six parabolas are evenly spaced around a circle. The parabolas open outward with their axes being extensions of six of the circle's radii. Parabola P1P_1 is tangent to P2P_2, which is tangent to P3P_3, which is tangent to P4P_4, which is tangent to P5P_5, which is tangent to P6P_6, which is tangent to P1P_1. What is the diameter of the circle?
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