MathDB

2003.11

Part of Ukraine Correspondence MO - geometry

Problems(1)

ВС/US = DE/SТ = FА/ТU if АВ/РR = CD/RQ= ЕF/QP, convex hexagon ABCDEF

Source: 2003 VIII All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-11 p11

1/10/2023
Let ABCDEFABCDEF be a convex hexagon, P,Q,RP, Q, R be the intersection points of ABAB and EFEF, EFEF and CDCD, CDCD and ABAB. S,T,UVS, T,UV are the intersection points of BCBC and DEDE, DEDE and FAFA, FAFA and BCBC, respectively. Prove that if ABPR=CDRQ=EFQP,\frac{AB}{PR}=\frac{CD}{RQ}=\frac{EF}{QP}, then BCUS=DEST=FATU.\frac{BC}{US}=\frac{DE}{ST}=\frac{FA}{TU}.
geometryhexagonratio