In an isosceles triangle ABC in which AC=BC and ∠ABC<60o, I and O are the centers of the inscribed and circumscribed circles, respectively. For the triangle BIO, the circumscribed circle intersects the side BC again at D. Prove that:
i) lines AC and DI are parallel,
ii) lines OD and IB are perpendicular. parallelperpendiculargeometryisosceles