ABC is a triangle in which $$\angle A$$ is obtuse. AD, BE and CF are the altitudes from A, B and C respectively to BC, CA and AB. $$A_1$$, $$B_1$$ and $$C_1$$ are arbitrary points on BC, CA and AB respectively. The circles on $$AA_1$$, $$BB_1$$ and $$CC_1$$ as diameters are drawn. Show that the lengths of the tangents from the orthocentre of $$\triangle ABC$$ to these circles are equal.