MathDB

4

Part of 2017 ITAMO

Problems(1)

ITAmo 2017, P4

Source: ITAmo 2017

5/5/2017
Let ABCDABCD be a thetraedron with the following propriety: the four lines connecting a vertex and the incenter of opposite face are concurrent. Prove AB⋅CD=AC⋅BD=AD⋅BCAB \cdot CD= AC \cdot BD = AD\cdot BC.
geometry