VTMO 2026 - Grade 7 - Semifinal - SET 9 - Self-study Question 25

Right triangle $ABC$ has $\angle A=90^\circ$, $AB=20$ cm and $AC=15$ cm. Points $D,E$ lie on $AB$ and $F,G$ lie on $AC$ in the order shown, with

$S_{ADF}:S_{DEF}:S_{EFG}:S_{EGB}:S_{BGC}=1:2:3:4:5$.

Find $ED^2+FG^2$.