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2015 points, equal segments, equal angles 2015 BMT Team 7

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January 4, 2022
geometryequal anglesequal segments

Problem Statement

X1,X2,...,X2015X_1, X_2, . . . , X_{2015} are 20152015 points in the plane such that for all 1≤i,j≤20151 \le i, j \le 2015, the line segment XiXi+1=XjXj+1X_iX_{i+1} = X_jX_{j+1} and angle ∠XiXi+1Xi+2=∠XjXj+1Xj+2\angle X_iX_{i+1}X_{i+2} = \angle X_jX_{j+1}X_{j+2} (with cyclic indices such that X2016=X1X_{2016} = X_1 and X2017=X2X_{2017} = X_2). Given fixed X1X_1 and X2X_2, determine the number of possible locations for X3X_3.
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