How do you derive the mirror equation with a convex mirror?

[Sciencelover91]

Homework Statement

Derive the mirror equation for a convex mirror (Si*So=f^2). Do not use a Ray heading toward the center of curvature point (C).
Si - distance between the object's image and the focal point.
So- distance between the object and the focal point.
Do- distance between the mirror and object.
Di- distance between the mirror and the object's image.
f- focal length

Homework Equations

1/do + 1/di = 1/f

The Attempt at a Solution

My work is all on the picture. I am trying to get to the equation SoSi=f^2 but I don't get the right equation so I am wondering if I made a mistake in my diagram?

 

[haruspex]

a mistake in my diagram?

Look at the ray you have starting horizontally. Where it hits the mirror, draw the normal to the mirror at that point. What should be the relationship between that incident ray, the normal, and the reflected ray?