Geometry Problems, Online Education

Problem 524: Circle, Equilateral Triangles, Midpoint, Side, Measurement. Level: High School, SAT Prep, College geometry

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 Formula to prove. Post a comment or solution.

Circle with equilateral triangles




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.

Circle, Tangent, Diameter, Radius, Congruence

Problem 525.
Circles, Diameter, Tangent, Radius, Congruence, Measurement.

Tangent Circles

Problem 523.
Tangent Circles, Diameter Perpendicular, Collinearity.

Geometry Problem: Right triangle, Circle, Tangent

Problem 522.
Right Triangle, Circle, Diameter, Tangent.

Triangle with Squares and Rectangles

Geometry problem 518

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