Hnh 1

Hnh 1

Bi 5 (3.5 im). Cho ng trn (O) v im A bn ngoi ng trn, t A v tip tuyn AB vi ng trn (B l tip im). K ng knh BC ca ng trn (O). AC ct ng trn (O) ti D (D khc C).

a) Chng minh BD vung gc AC v AB2 = AD . AC.1CM: BD vung gc AC0.5

CM: ABC vung ti A0.25

CM: AB2 = AD . AC0.25

b) T C v dy CE // OA. BE ct OA ti H. Chng minh H l trung im BE v AE l tip tuyn ca ng trn (O).1CM: H trung im BE0.5

CM: AE l tip tuyn ca ng trn (O) 0.5

c) Chng minh . 0.75CM: OC2 = OH . OA (= AB2)0.25

CM: OCH ~ OAC0.25

(

0.25

d) Tia OA ct ng trn (O) ti F. Chng minh FA . CH = HF . CA.0.75CM:

0.25

CM:

0.25

CM: CF l ng phn gic ca .

Hnh 2

CM: FA . CH = HF . CA

Nu c ,

Nn

Vy t gic ACDB l hnh thang

M

Suy ra t gic ACDB l hnh thang vung

c/m OD l ng trung trc ca BM

nn suy ra BD2 = DN.DO

c/m suy ra BD2 = DE.DA

Vy DE.DA = DN.DO

c/m (gcg) OF = BDc/m OF // BD

Nn OFDB l hnh bnh hnh

c gc DBO = 900 nn OFDB l hnh ch nht

c/m u

EMBED Equation.DSMT4

EMBED Equation.DSMT4

EMBED Equation.DSMT4 Tnh ng AC =

c/m v Tnh ng DB =

tnh ng SACDB =

hnh 3

a)(ACB ni tip ng trn (O) c AB l ng knh ( (ACB=900

(AEH ni tip ng trn (O1) c AH l ng knh ( (AEH=900

(BFH ni tip ng trn (O2) c BH l ng knh ( (BFH=900

Chng minh t gic CEHF c ba gc vung nn l hnh ch nht

b)(AHC vung ti H c HE l ng cao ( CE.CA = CH2

(BHC vung ti H c HF l ng cao ( CF.CB = CH2

(ACB vung ti C c CH l ng cao ( HA.HB = CH2

( CE.CA = CF.CB = HA.HB

c)Gi J l giao im hai ng cho ca hnh ch nht CEHF

Chng minh (O1EJ = (O1HJ (ccc)

Chng minh c EF l tip tuyn ca (O1)

Chng minh tng t EF l tip tuyn ca (O2)

d)BC ct AM ti K

Chng minh M l trung im ca AK.

BJ ct AK ti M, chng minh M l trung im ca AK

Kt lun BM, CH, EF ng quy ng quy ti J.

F

D

C

M

E

N

B

A

O

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