Let ABC be a triangle with ∠ABC=90∘ and AB its shortest side. Denote by H the intersection of the altitudes of triangle ABC. Let K be the circle through A with centre B. Let D be the other intersection of K and AC. Let K intersect the circumcircle of BCD again at E. If F is the intersection of DE and BH, show that BD is tangent to the circle through D, F, and H. circlesgeometrytangentcircumcircle