ΔABD dreptunghic: m(<A)=90°⇒T.P.⇒ AD²=BD²-AB²
AD²=36-16
AD²=20⇒AD=2√5 cm
Notam AE∩BD={M}
ΔABD dreptunghic | m(<A)=90°
| AD=2√5 cm ⇒ sin(ABD)=AD/BD=√5/3
| BD=6 cm
ΔAMB dreptunghic:sin(ABD)=sin(ABM)= √5/3
Dar sin (ABM)= AM/AB
Din ambele relatii⇒AM/AB=√5/3
AM=4√5/3 cm
ΔAMD dreptunghic:m(<M)=90°⇒ DM²=AD²-AM²
DM²=20-80/9
DM²=100/9⇒DM=10/3 cm
Deoarece M∈(BD)⇒MB=BD-DM⇒MB=8/3
DE || AB⇒TFA⇒ΔMDE ≈ΔMBA⇒MD/MB=DE/AB=ME/MA⇒
⇒10/8=DE/4⇒DE=5 cm
ΔDAE dr:m(<D)=90°⇒AE²=AD²+DE²
AE²=20+25
AE²=45⇒AE=3√5 cm
CE=DE-DC⇒CE=1 cm
CE||AB⇒(TFA)⇒ΔABP≈ΔECP⇒AB/CE=AP/PE=BP/CP=k⇒ k=4 (deoarece AB/CE=4/1)
Aabp/Acep=k²⇒Aabp/Acep=16
