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If $A (x_{1}, y_{1}), B (x_{2}, y_{2}),$ and $C (x_{3}, y_{3})$ are three non-collinear points such that $x 12 + y 12 = x 22 + y 22 = x 32 + y 32,$ then prove that $x_{1} sin 2 A + x_{2} sin 2 B + x_{3} sin 2 C = y_{1} sin 2 A + y_{2} sin 2 B + y_{3} sin 2 C = 0 .$

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A (x_{1}, y_{1}), B (x_{2}, y_{2}),

and

C (x_{3}, y_{3})

are three non-collinear points such that

x 12 + y 12 = x 22 + y 22 = x 32 + y 32,

then prove that

x_{1} sin 2 A + x_{2} sin 2 B + x_{3} sin 2 C = y_{1} sin 2 A + y_{2} sin 2 B + y_{3} sin 2 C = 0 .

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Question Text

A (x_{1}, y_{1}), B (x_{2}, y_{2}),

and

C (x_{3}, y_{3})

are three non-collinear points such that

x 12 + y 12 = x 22 + y 22 = x 32 + y 32,

then prove that

x_{1} sin 2 A + x_{2} sin 2 B + x_{3} sin 2 C = y_{1} sin 2 A + y_{2} sin 2 B + y_{3} sin 2 C = 0 .

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