I am a little bit confused. I drawn a concave spherical mirror and here is what I have drawn by Geogebra
As you can see, the angle DAC = angle ADC ( both equal to the incident angle because the normal line AD go through A). Similarly, angle AEC = angle CAE. I induced that CA = CD = CE. However, this is impossible because C is not the center of the mirror ( A is )
If I move the focal to the center of the mirror, and the point we call " center of curvature" to the B point in the following picture, I got a reasonable picture:
Could someone please explain why did I wrong, thank you!
Your first figure is the correct one. The issue is that the rules are precise for parabolic mirrors, not spherical mirrors. A spherical mirror gives a pretty good approximation if you restrict yourself to a limited amount of its curvature. For example, in your top image, imagine the mirror extending no further than E on either side of B.