

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 C_{1}. The point D is the midpoint
of BC and E and F are on the circle C_{1}. If the
triangle DEF is equilateral (side x), prove that
.
Post a comment or solution.
Reference: Fukagawa Hidetoshi, Tony Rothman, "Sacred Mathematics: Japanese Temple Geometry" (Princenton
University Press, 2008).


See also:


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

Problem 523.
Tangent Circles, Diameter Perpendicular, Collinearity. 

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






