Mathegoras

Coordinate geometry › Circles in coordinates › Centre and radius

Sums of squares on a unit circle

High school · ●●●○○ 50 pts

Three points A(x1,y1)A(x_1, y_1), B(x2,y2)B(x_2, y_2), C(x3,y3)C(x_3, y_3) lie on the unit circle x2+y2=1x^2+y^2=1 and satisfy x1+x2+x3=0x_1+x_2+x_3=0 and y1+y2+y3=0y_1+y_2+y_3=0. Find x12+x22+x32x_1^2+x_2^2+x_3^2 and y12+y22+y32y_1^2+y_2^2+y_3^2.

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unit circletrigonometric identitiesdouble angle formulaequilateral triangle