Răspuns:
ΔADC - dreptunghic isoscel ⇒ ∡ACD = ∡DAC = 45°
ΔABO - isoscel ⇒∡DAB=∡ABO
BE - bisectoare ⇒∡ABO =∡CBE
⇒∡DAB=∡ABO=∡CBE
ΔADB - dreptunghic in D ⇒∡DAB+∡ABO+∡CBE = 90°
⇒3·∡DAB=90°
⇒∡DAB=∡ABO=∡CBE = 30°
⇒∡BAC=∡DAC+∡DAB = 45°+30° = 75°
∡ABC = 2·∡ABO = 60°
deci: in ΔABC: ∡A=75°, ∡B = 60°, ∡C = 45°
∡BOD = 90°-∡CBE = 90°-30° = 60°
∡BOD = 60°
