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Problem 524: Circle, Equilateral Triangles, Midpoint, Side, Measurement. Level: High School, SAT Prep, College geometry
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The figure shows an equilateral
triangle ABC (side a) inscribed in a circle C1. The point D is the midpoint
of BC and E and F are on the circle C1. If the
triangle DEF is equilateral (side x), prove that
 .
Post a comment or solution.
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References:
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Reference: Fukagawa Hidetoshi, Tony Rothman, "Sacred
Mathematics: Japanese Temple Geometry" (Princenton
University Press, 2008).
Between the seventeenth and nineteenth centuries Japan was totally isolated from the West by imperial decree. During that time, a unique brand of homegrown mathematics flourished, one that was completely uninfluenced by developments in Western mathematics. People from all walks of life—samurai, farmers, and merchants—inscribed a wide variety of geometry problems on wooden tablets called sangaku and hung them in Buddhist temples and Shinto shrines throughout Japan. |
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Problem 525.
Circles, Diameter, Tangent, Radius, Congruence, Measurement. |
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Problem 523.
Tangent Circles, Diameter Perpendicular, Collinearity. |
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Problem 522.
Right Triangle, Circle, Diameter, Tangent. |
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