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4 July, 10:34

Three identical coins, labeled A, B, and C in the figure, lie on three corners of a square 10.0 cm on a side. Determine the x coordinate of each coin, xA, xB, and xC.

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  1. 4 July, 11:14
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    The line of symmetry of the triangle bisects the right angle and the diagonal of the square.

    The line is 1/2 the length of the square's diagonal:

    (1/2) (10√2) = 5√2.

    Let CG be a distance x from the vertex of the right angle in the triangle.

    Remaining distance = 5√2 - x.

    (1) (x) = (2) (5√2 - x)

    x = 10√2 - 2x

    3x = 10√2

    x = (10/3) √2.

    Using Pythagorean theorem,

    x^2 + y^2 = c^2

    c = (10/3) √2,

    and x = y,

    so 2x^2 = 200/9

    x = √ (100/9) = 10/3 = y.

    x = y = 3.333
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