Holiday Contest 2025 - Team Round - Problem 18

Let \triangle ABC be an isosceles triangle with AB = AC. Let \gamma denote the arc CAB of the circumcircle of \triangle ABC and let \gamma' be the reflection of \gamma across BC. Let I be the center of the circle tangent to AB, AC, and internally tangent to \gamma'. Let D be the midpoint of AI. Given that \angle ADC = 97^\circ, find \angle CAB in degrees.