Hello, GreenDay14!

I have an analytic proof . . .

Through a point on the diagonal of a square,

lines are drawn parallel to the sides; being on the sides.

Prove that these four points are concyclic. Code:

| Q
(0,a)| (b,a) (a,a)
- - - - - - o - -
| | * |
P | | * | R
(0,b) o - - - - - - * - - o (a,b)
| * | |
| o | |
| * C | |
| * | |
| * | |
| * | |
- - - - - - - - - o - - - - -
(0,0) (b,0) (a,0)
S

Let = side of the square.

Let be the point on the diagonal.

Then we have: .

Let be the center of the square.

Find the distances: .

. .

. .

. .

. .

We find that they are *all* equal to: .

Hence, there is a point equidistant from

. . is the circumcenter of quadrilateral

Therefore, are concyclic.