## IMO 2018 P6

Discussion on International Mathematical Olympiad (IMO)
M Ahsan Al Mahir
Posts: 16
Joined: Wed Aug 10, 2016 1:29 am

### IMO 2018 P6

A convex quadrilateral $ABCD$ satisfies $AB\cdot CD = BC\cdot DA$. Point $X$ lies inside $ABCD$ so that $\angle{XAB} = \angle{XCD}\quad\,\,\text{and}\quad\,\,\angle{XBC} = \angle{XDA}.$Prove that $\angle{BXA} + \angle{DXC} = 180^\circ$.