VTMO 2026 - Grade 9 - Semifinal - SET 3 - Self-study Question 1

In the figure, triangle ABC is right-angled at A, H lies on BC with $AH\perp BC$, K lies on AC, and I is the foot of the perpendicular from A to BK. Given $AB=2BH$, find $\angle BIH+\angle BCA$.