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.

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