Square_Inscribed_quadrangle

Quadrangle inscribed in a square

Given are points A, B, C, D on different sides of a square. Let CE be orthogonal to the diagonal ĀD from C. Then |CE| = |BD|. In fact if we rotate the quadrangle t=(ABCD) about the square's center Ļ, by 90 degrees, then the diagonal BD will take the position Ā'D', orthogonal to BD. CE is parallel and equal to B'D'.

For an application of this proposition, constructing squares whose sides pass through 4 given points, look at the file: Squares_through_4_points.html .

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