VTMO 2026 - Grade 7 - Final - SET 8 - Self-study Question 4

a) Equal segments $AB$ and $CD$ intersect at $K$, and $AC\parallel BD$. Prove that $KA=KC$.

b) Triangle $ABC$ is isosceles at $A$. Its angle bisector $BD$ meets $AC$ at $D$. Altitude $AH$ satisfies $AH=\dfrac12BD$. Find $\angle BAC$.