In acute triangle ABC,AB<AC, I is its incenter, D is the foot of perpendicular from I to BC, altitude AH meets BI,CI at P,Q respectively. Let O be the circumcenter of △IPQ, extend AO to meet BC at L. Circumcircle of △AIL meets BC again at N. Prove that CDBD=CNBN. geometryincentercircumcircle