Finding the point on line where two points join at equal angles to a perpendicular line

Question

Im not sure what this would be called and how to explain it properly, so I drew an image to represent what I mean: (cant embed it yet)

https://i.stack.imgur.com/0QKge.png

Basically, I want to find point C where the angles from a perpendicular line in between are the same. How would I find out what C's coordinates are? (the black line at the top is at y=0)

Thank you :)

Answer 1

Find the symmetric $A'$ of $A$ wrt the horizontal axis and connect $B$ with $A'$

Answer 2

You can use the fact that if the two angle are the same also the tangebts of the angles are the same, so, if $C=(x,y)$ we have $$ \frac{y-100}{x-100}=\frac{500-y}{500-x} $$

If you know $y$ you can find $x$.