Trigonometry: Find points coordinates in equally arms triangle

Question

h have a equally arms triangle. The angle on point C is not 90 degrees.

I have:

1. The coordinates of point $C(C_x, C_y)$
2. The coordinates of the end point of $h$, $H(H_x, H_y)$
3. The length of $C$ (example: 20)

I need to find the coordinates of point $A(A_x, A_y)$ and $B(B_x, B_y)$.

My project is drawing a line from a node to a point in space (in red):

I know the position of the node $C(C_x, C_y)$ ("No name" red circle) and the point the line is drawn to $H(H_x, H_y)$

I need to coordinates of 2 equally distant points (in green) around the H point. I want to set the length of distance from the H point to the green points.

Can anyone help?

Answer 1

Assuming $H = (H_x, H_y)$ is the point in the middle of $A$ and $B$, then $H_y = A_y = B_y$.

Further $A_x = C_x - c/2$, $B_x = C_x + c/2$.