1、 2016 年中考专题：几何最值问题 （二） 1 2 3 4 5 1 ABCD 1cm M N BC CD AM MN BM= cm ABCN cm 2 2 AB 2 C AB AC BC AB ACD BCE DE 3 ABCD AB=2 AD=3 P BC P B C P P PE CD E. (1) AE BP (2) BP x CE y y x x y (3) BP . 4 ABCD AB=5 BC=10 F AD E 1 = 60 CE 2 60 90 k EFD=k AEF k CF CE 2 CF 2 tan DCF 5 4 ABCD P AD A D B P C G PG DC
2、 H EF BP BH 1 APB= BPH 2 P AD PDH 3 AP x EFGP S S x S 6 1 O 2 O CD 1 O 2 OC 2 OD A B 2 CO D 60 E F 12 OO 1 O 2 O CD EF=24cm 1 O x cm x 2 O CD 1 O 2 O CD 0.45 2 /cm 0.06 2 /cm 1 O O 1 O 2 A B F D E C 1 ABCD AB=6 AD=9 E CD (E D ) E AD F( E C EF AC ) EF D G DE=x ABCD y (1) CD (2) G BC x (3) y x x y ? ?
3、 2 O AC BD AC=10 BD=6 E M AB O EF MN 1 h 2 h 1 S 2 EH MQ 1 h 2 h 2 h 3 2 ABCD P AB Q CD DQ t PQ AD BC M N Q E M F 1 2 P M Q N PMQN S S t S 1 AC 4cm C A C B A A 43 cm ! B 8cm 8cm C 16 3 cm ! D 8 3 cm ! 2 OA B OB=AB P A C D 3 AC=3 P BC AP A 3.5 B 4.2 C 5.8 D 7 4 1 2 AB=13 BC=14 5 13 1 H AH= AC= S = 2
4、D AC A C A C BD E F BD=x AE=m CF=n D A S =0 1 x m n S S 2 m+n x m+n 3 x D x A B C 5 1 4 AB CD 6 M AB 1 0 AB CD AB CD MN AB MN=8 P P CD 1 M AB CD 2 N CD 1 NOP MOP M AB CD 1 3 P CD 2 4 MOP P CD ! c ! ! 6 1 AC=1 BC=2 1 2 AB X CB Y 2 2 P P S S S S 7 140m 100m 95m 90m A B C D 8 C 1B1C (1) 1 1 A1B1 BC D 1
5、CD (2) 2 AA1 BB1 1 1 S1 S2 S1 2 (3) 3 AC E A1B1 P AC a EP (4)EP 9 1 O l 2 l A B AB A 1 B 2 C 3 D 2 10 A B 1 A O 600cm B O 300cm AO (AO ) 20cm/ AO (AO ) 10cm/ (1) B ( ) (3 ) (2) B ( ) (3 ) (3) 2 E OA P A B (3 ) ( 2 3 5 6 1. 1 2 5 8 BM=xcm MC=1 xcm AMN=90 AMB+ NMC=90 NMC+ MNC=90 AMB=90 NMC= MNC ABM MC
6、N AB BM MC CN 1x 1 x CN CN=x 1 x 22 ABCN 1 1 1 1 1 1 5 S 1 1 x 1 x x x x 2 2 2 2 2 2 8 1 2 0 x= 1 2 cm S ABCN 5 8 cm 2 2. 1 AC x BC 2 x ACD BCE DCA 45 ECB 45 DC 2 x 2 CE 2 (2 x) 2 DCE 90 DE 2 DC 2 CE 2 2 x 2 2 2 (2 x) 2 2 x 2 2x 2 (x 1) 2 1 x 1 DE 2 DE 1 3. 1 AB=2 2 2 2 2 AP AB 3 2 5 2 AB BP PC CE 2
7、x 3 x y 2 13 y x x 22 22 1 3 1 3 9 y x x (x ) 2 2 2 2 8 3 x 2 y 9 8 2 BP=x, 2 2 13 CE x x 22 CP CE CB CD 2 13 xx 3x 22 32 2 3x 13x 12 0 1 4 x 3 2 x3 BP= 4 3 4. 1 = 60 BC=10 si n = CE BC sin60 = CE 3 10 2 CE=53 2 k=3 EFD=k AEF CF BA G F AD AF=FD ABCD AB CD G= DCF AFG CFD G= DCF G= DCF AF=FD AFG CFD A
8、AS CF=GF AG=CD CE AB EF=GF AEF= G AB=5 BC=10 F AD AG=5 AF= 1 2 AD= 1 2 BC=5 AG=AF AFG= G AFG EFC= AEF+ G=2 AEF CFD= AFG CFD= AEF EFD= EFC+ CFD=2 AEF+ AEF=3 AEF k=3 EFD=3 AEF BE=x AG=CD=AB=5 EG=AE+AG=5 x+5=10 x Rt BCE CE 2 =BC 2 BE 2 =100 x 2 Rt CEG CG 2 =EG 2 +CE 2 = 10 x 2 +100 x 2 =200 20x CF=GF C
9、F 2 = 1 2 CG 2 = 1 4 CG 2 = 1 4 200 20x =50 5x CE 2 CF 2 =100 x 2 50+5x= x 2 +5x+50= x 5 2 2 +50+ 25 4 x= 5 2 E AB CE 2 CF 2 EG=10 x=10 5 15 = 22 CE= 2 25 5 15 100 x = 100 = 42 5 15 CG 15 2 tan DCF tan G 15 EG 3 2 5. 1 1 PE=BE EBP= EPB EPH= EBC=90 EPH EPB= EBC EBP PBC= BPH AD BC APB= PBC APB= BPH 2
10、PHD 8 2 B BQ PH Q 1 APB= BPH A= BQP=90 BP=BP ABP QBP AAS AP=QP AB=BQ AB=BC BC=BQ C= BQH=90 BH=BH BCH BQH HL CH=QH PHD PD+DH+PH=AP+PD+DH+HC=AD+CD=8 3 3 F FM AB M FM=BC=AB EF EF BP EFM+ MEF= ABP+ BEF=90 EFM= ABP A= EMF=90 AB=ME EFM BPA ASA EM=AP=x Rt APE 4 BE 2 +x 2 =BE 2 2 x BE 2+ 8 2 x CF BE EM 2+ x
11、 8 PEFG BEFC 2 2 2 1 1 x 1 1 S BE CF BC= 4+ x 4= x 2x+8= x 2 +6 2 2 4 2 2 1 04 2 x=2 S 6 6. 1 O1A 1 O2C O2D A B 1 2C O2E 2D 2 CO D 60 2O1= 1 2 2 1AO2 1 21 12 AO sin AO O OO 1O2=A O1 2O1 2=EF EO1 O1O2=24 3x O2CD 24 3x cm 2 y 2 22 360 60 24 3x y 0.45 x 0.06 0.9 x 7.2 x 28.8 360 2 0.9 x 4 14.4 x=4 y 1
12、4cm 1 1 CD=33 1=30 2 G BC GE=DE=x EC=33 x 1=30 FED=60 GEF=60 GEC=60 GE=2CE 2(3 3 ) xx 23 x 3 EFG EFD 2 13 22 EFD y S DE DF x 1 0 2 3 x x 23 x 63 ( 25 3) A B C D E F G 1 M N L K S E R O A B M 2 23 x EFG 3 GE=DE=x EC=33 x 2(3 3 ) ME x 2(3 3 ) 3 6 3 GM GE ME x x x NG= 3 6 3 36 3 x x 2 1 1 3 ( 3 6)(3 6
13、3) ( 3 6) 2 2 2 MNG S NG MG x x x 222 1133 (36)3(6318) 2222 EFDMNG ySSDEDFNGMGxxxx = 22 3( 6 3 18) 3( 3 3) 9 3 x x x 33 x max 93 y 33 x max 93 y 2 1 ABCD . / EF BD ABD AEF 1 5 65 h EF 1 6 5 5 EF h 2 1 1 1 1 6 6 5 15 25 5 5 2 2 OEF S S EF h h h h 1 5 2 h max 15 2 S . 2 OE OM . OR AB R OB OR OS 1 , EM
14、 , OE OM OR RE RM . 22 5 3 34 AB 15 34 OR 2 2 15 9 3 34 34 BR / / ML EK OB , OK BE OL BM OA AB OA AB 2 OK OL BE BM BR OA OA AB AB AB 12 9 5 5 17 hh 12 45 17 hh 1 h 1 45 0 17 h 1 45 34 h 2 , EM 12 hh 1 h 1 05 h . 3 1 ABCD A B D 90 AD AB QE AB MF BC AEQ MFB 90 ABFM AEQD MF AB QE AD MF QE PQ MN EQP FMN QEP MFN 90 PEQ NFM 2 P AB AB 2 DQ AE t PA 1 PE 1 t QE 2 PQ 2 2 PE QE 4 ) 1 ( 2 t PEQ NFM MN PQ 4 ) 1 ( 2 t PQ MN S MN PQ 2 1 4 ) 1 ( 2 1 2 t 2 1 t 2 t 2 5 0 t 2 t 1 S 2 S 2 1 t 2 t 2 5 S 2 1. D A C CA A C B 4 120 4 8 180 3 AA L cm D 2. A P
