MathDB

P15

Part of 2023 China Team Selection Test

Problems(1)

Orz Orz Orz Orz Orz Geometry II, and also orz i3435.

Source: China TST 2023 Problem 15

3/27/2023
For a convex quadrilateral ABCDABCD, call a point in the interior of ABCDABCD balanced, if
(1) PP is not on AC,BDAC,BD
(2) Let AP,BP,CP,DPAP,BP,CP,DP intersect the boundaries of ABCDABCD at A′,B′,C′,D′A', B', C', D', respectively, then
AP⋅PA′=BP⋅PB′=CP⋅PC′=DP⋅PD′AP \cdot PA' = BP \cdot PB' = CP \cdot PC' = DP \cdot PD'
Find the maximum possible number of balanced points.
geometry