Problem

Source: Sharygin 2018 Grade 9 Day 2 Problem 9.6

Tags: incenter, excenter, diagonals, geometry, circumscribed quadrilateral



Let $ABCD$ be a circumscribed quadrilateral. Prove that the common point of the diagonals, the incenter of triangle $ABC$ and the centre of excircle of triangle $CDA$ touching the side $AC$ are collinear.