Question

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.

Answer 1

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