trisecting sides + constructing similar triangles - Austrian-Polish 2003
Source:
May 18, 2019
geometrysimilar trianglesSegment
Problem Statement
ABC is a triangle. Take a=BC etc as usual.
Take points T1,T2 on the side AB so that AT1=T1T2=T2B. Similarly, take points T3,T4 on the side BC so that BT3=T3T4=T4C, and points T5,T6 on the side CA so that CT5=T5T6=T6A.
Show that if a′=BT5,b′=CT1,c′=AT3, then there is a triangle A′B′C′ with sides a′,b′,c′ (a′=B′C' etc).
In the same way we take points Ti′ on the sides of A′B′C′ and put a′′=B′T6′,b′′=C′T2′,c′′=A′T4′.
Show that there is a triangle A′′B′′C′′ with sides a′′b′′,c′′ and that it is similar to ABC.
Find a′′/a.