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For some ellipses it is possible to inscribe seven circles, such that each circle is tangential to the ellipse at precisely two points, and such that successive circles are tangential …

The figure shows a triangle $ABC$ and its incircle. $\triangle ABC$ has integer side lengths. If $CF = FB$ and $AG = GH = HF$, what is its smallest possible …

The figure shows a regular pentagon inscribed in an isosceles triangle. One side of the pentagon rests on the base of the triangle, while two pentagon vertices touch the legs …

The three small circles shown in the figure are congruent. If the ratio of the radius of a small circle to the radius of the large circle can be expressed …

The polynomial $f(x) = x^{52} + a_1x^{51} + a_2x^{50} + \cdots + a_{51}x+a_{52}$ has roots $\tan\theta_1, \tan\theta_2, \tan\theta_3, \ldots, \tan\theta_{52}.$

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