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Bi ton
Bi ton. Cho tam gic nhn ABC, O l tm ng trn ngoi tip, D, E, F theo th t l trung im ca BC, CA, AB. im M thuc ng thng BC. N l giao im ca AM v EF. P l giao im th hai ca ON v ng trn (ODM). Dng im Q sao cho QPMD l hnh bnh hnh. Chng minh rng Q thuc ng trn (DEF).
Li gii.
Bi ton. Cho tam gic nhn ABC, O l tm ng trn ngoi tip. D, E, F theo th t l trung im ca BC, CA, AB. M thuc ng thng EF. N l giao im ca AM v BC. S l giao im th hai ca OM v ng trn (ODN). Dng im R sao cho RSND l hnh bnh hnh. Chng minh rng R thuc ng trn (DEF).
Li gii.Gi (O) l ng trn ngoi tip H l im i xng ca D qua O; K l giao im ca AD v EF; L l im i xng ca M qua K (h.1).
D thy O, H theo th t l trc tm ca cc tam gic DEF, AEF (1).
T , ch rng K l trung im ca EF, suy ra
D thy
Do T , ch rng K l trung im ca EF, suy ra
T (1), (2) v (3) suy ra Do
(h.1)
iu c ngha l R thuc ng trn ng knh DH.
Ni cch khc R thuc (O). _1495802519.unknown
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