Let ABC be an acute triangle with AC>AB and O its circumcenter. Let D be a point on segment BC such that O lies inside triangle ADC and ∠DAO+∠ADB=∠ADC. Let P and Q be the circumcenters of triangles ABD and ACD respectively, and let M be the intersection of lines BP and CQ. Show that lines AM,PQ and BC are concurrent.Pablo Jaén, Panama geometrycircumcircleconcurrencyIberoamerican