Proposed Problem

See complete Problem 257 at:

gogeometry.com/problem/p257_equilateral_triangle_circumcircle_distance_sides.htm

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

## Tuesday, February 24, 2009

### Problem 257: Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances, Squares

Labels:
circumcircle,
distance,
equilateral,
side,
square,
triangle

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By an earlier problem, we know that d = e + f

ReplyDeletehence, LHS =(e+f)^2+e^2+f^2 = 2(e^2+f^2+ef)

Using cosine rule in Tr. BDC, we've: a^2 =e^2+f^2-2efcos(BDC)=e^2+f^2-2ef(-1/2)=e^2+f^2+ef

Hence, LHS = 2(e^2+f^2+ef) = 2a^2

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