MathDB

P6

Part of 2022 Serbia Team Selection Test

Problems(1)

Weird geometry

Source: Serbia TST 2022, Problem 6 (source: https://dms.rs/wp-content/uploads/2022/05/ZADACI_IZBORNO_IMO_2022.pdf)

5/1/2023
Let ABCDABCD be a trapezoid with bases AB,CDAB,CD such that CD=k⋅ABCD=k \cdot AB (0<k<10<k<1). Point PP is such that ∠PAB=∠CAD\angle PAB=\angle CAD and ∠PBA=∠DBC\angle PBA=\angle DBC. Prove that PA+PB≤11−k2⋅ABPA+PB \leq \dfrac{1}{\sqrt{1-k^2}} \cdot AB.
geometrytrapezoid