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a) BC^2 = AB^2 + AC^2 = 15^2 + 20^2 = 625 ---> BC = 25 (cm) 
1/AH^2 = 1/AB^2 + 1/AC^2 = 1/225 + 1/400 = 625 / (225.400) 
---> 1/AH = 25/(15.20) = 1/12 ---> AH = 12 (cm) 
b) Ha EF _I_ BC (F thuoc BC)
Tu giac AEFH co AE // HF (vi ADCE la hinh binh hanh) ; AH // EF va ^H = 90*
---> AEFH la hinh binh hanh ---> AE = HF ; AH = EF va AE // HF hay AE // BC
HC = HD + DC = BH + AE = BH + HF (1)
Mat khac HC = FC + HF (2)
(1),(2) ---> BH = FC
Hai tam giac AHB va EFC bang nhau (vi BH = FC, ^H = ^F, AH = EF) ---> ^ABC = ^ECB
Tu giac ABCE co AE // BC va ^ABC = ^ECB ---> ABCE la hinh thang can.
c) AC = 20, AB = 15, AH = 12 ---> HC = 16, BH = 9 (tinh bang d/ly Pythagore)
AE = HF = HC - FC = HC - BH = 16 - 9 = 7 (cm)

d) S(ABCE) = (1/2)(AE + BC).AH = (1/2)(7 + 25).12 = 192 (cm^2).