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  2. Special cases of Apollonius' problem - Wikipedia

    en.wikipedia.org/wiki/Special_cases_of_Apollonius...

    In general, the same inversion transforms the given line L and given circle C into two new circles, c 1 and c 2. Thus, the problem becomes that of finding a solution line tangent to the two inverted circles, which was solved above. There are four such lines, and re-inversion transforms them into the four solution circles of the Apollonius problem.

  3. List of circle topics - Wikipedia

    en.wikipedia.org/wiki/List_of_circle_topics

    This list of circle topics includes things related to the geometric shape, either abstractly, as in idealizations studied by geometers, or concretely in physical space. It does not include metaphors like "inner circle" or "circular reasoning" in which the word does not refer literally to the geometric shape.

  4. Problem of Apollonius - Wikipedia

    en.wikipedia.org/wiki/Problem_of_Apollonius

    Figure 1: A solution (in purple) to Apollonius's problem. The given circles are shown in black. Figure 2: Four complementary pairs of solutions to Apollonius's problem; the given circles are black. In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1).

  5. Nine dots puzzle - Wikipedia

    en.wikipedia.org/wiki/Nine_dots_puzzle

    The "nine dots" puzzle. The puzzle asks to link all nine dots using four straight lines or fewer, without lifting the pen. The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen.

  6. Gauss circle problem - Wikipedia

    en.wikipedia.org/wiki/Gauss_circle_problem

    This problem is known as the primitive circle problem, as it involves searching for primitive solutions to the original circle problem. [9] It can be intuitively understood as the question of how many trees within a distance of r are visible in the Euclid's orchard , standing in the origin.

  7. Tangent lines to circles - Wikipedia

    en.wikipedia.org/wiki/Tangent_lines_to_circles

    Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs. Since the tangent line to a circle at a point P is perpendicular to the radius to that point, theorems involving tangent lines often involve radial lines and orthogonal circles.

  8. Today's Wordle Hint, Answer for #1252 on Friday, November 22 ...

    www.aol.com/lifestyle/todays-wordle-hint-answer...

    If you’re stuck on today’s Wordle answer, we’re here to help—but beware of spoilers for Wordle 1252 ahead. Let's start with a few hints.

  9. Dividing a circle into areas - Wikipedia

    en.wikipedia.org/wiki/Dividing_a_circle_into_areas

    The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.

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