Let $ABC$ be a triangle where$\angle$B=55 and $\angle$ C = 65. D is the mid-point of BC. Circumcircle of ACD and ABD cuts AB and AC at point F and E respectively. Center of circumcircle of AEF is O. $\angle$FDO = ?
Source: BdMO 2020 Final Primary Category Problem 8
Tags: geometry, analytic geometry
Let $ABC$ be a triangle where$\angle$B=55 and $\angle$ C = 65. D is the mid-point of BC. Circumcircle of ACD and ABD cuts AB and AC at point F and E respectively. Center of circumcircle of AEF is O. $\angle$FDO = ?