P=96 cm
AB+AC+BC=96
2AB=60
AB=AC=30 cm
OD=OE
BD=DC=18 cm
In ΔADB aplicam Pitagora (suma catetelor la patrat este egala cu ipotenuza la patrat)
AB²=BD²+AD²
900=324+AD²
AD²=576
AD=24 cm
OE=OD
CO latura comuna ⇒ I.C ⇒ ΔCEO≡ΔCDO⇒ CE=CD
CE=18 cm⇒ AE=12 cm
ΔAEO~ΔADC⇒
[tex]\frac{AE}{AD} =\frac{AO}{AC}=\frac{OE}{CD}\\\\[/tex]
[tex]\frac{AE}{24} =\frac{AO}{30}=\frac{OE}{18}[/tex]
[tex]\frac{12}{24}=\frac{AO}{30} =\frac{OE}{18}[/tex]
AO=15 cm
OE=9 cm
OD=9 cm
Raspuns: b) 9 cm
Un alt exercitiu de geometrie gasesti aici: https://brainly.ro/tema/9676766
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