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    Category: Mini Course

    Catriona Shearer
    Website

    Catriona Shearer is a UK teacher who has received prominence on Twitter for posting various colorful geometry puzzles over the years.

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    Beautiful Geometry 1

    Section: Educational Category: Mini Course
    Tags: Geometry

    Example Problems

    What fraction of the hexagon is shaded?
    Which area is larger, the yellow or the red one?
    What is the area of the large square?
    What fraction of the outer circle is shaded?
    If the circle radius is 1, what area is shaded?
    What fraction of the decagon is shaded?
    1 2 3
    Catriona Shearer and Puzzle Prime August 11, 2000

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    Forum Description

    Example Problems

    What fraction of the hexagon is shaded?
    Which area is larger, the yellow or the red one?
    What is the area of the large square?
    What fraction of the outer circle is shaded?
    If the circle radius is 1, what area is shaded?
    What fraction of the decagon is shaded?

    Angles Inside a Quadrilateral

    What’s the angle?

    Let the quadrilateral be [latex]ABCD[/latex]. Using the provided angles, we can find that [latex]∠BCA=90°[/latex] and therefore point [latex]C[/latex] belongs to the circle with diameter [latex]AB[/latex]. Also, we can see that [latex]△AOD[/latex] is isosceles, [latex]OA=OD=OB[/latex], and point [latex]D[/latex] also lies on the circle with diameter [latex]AB[/latex].

    Using the provided angles, we can find that [latex]∠BCA=90°[/latex] and therefore point [latex]C[/latex] belongs to the circle with diameter [latex]AB[/latex]. Also, we can see that [latex]△AOD[/latex] is isosceles, [latex]OA=OD=OB[/latex], and point [latex]D[/latex] also lies on the circle with diameter [latex]AB[/latex].

    Therefore, [latex]ABCD[/latex] is inscribed in a circle with center [latex]O[/latex], and [latex]∠ACD=∠AOD/2=40°[/latex].

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