Cau a
Ta co:
1/AH^2 = 1/AB^2 + 1/AC^2
=> 1/AH^2 = 1/15^2 + 1/20^2
=> AH = 12
Xet tu giac AMHN ta co:
Goc A = goc AMH = goc ANH = 90
=> AMHN la hinh hinh chu nhat
=> AH = MN = 12
Cau b
Tu giac AMHN la hinh chu nhat
=> AH vuong goc MN
Ma AH vuong goc BC
=> BC song song MN
=> Goc AMN = goc ABC
=> Goc ANM = goc ACB
Xet tam giac AMN va tam giac ABC, ta co:
+) Goc A = 90 chung
+) Goc AMN = goc ABC
+) Goc ANM = goc ACB
=> Tam giac AMN dong dang tam giac ABC
=> AM.AB = AN.AC